Change array dimensions, using spreadsheet functions, when used inside SUMPRODUCT - arrays

Question

I am interested in spreadsheet functions, not VBA solutions, to be included in a single cell formula.
[A1:A15 contain numeric values from 1 to 127, B1:B15 contain integers from 1 to 7 that set a divisor.]
Given the function:
=SUMPRODUCT(MOD(FREQUENCY(A1:A15;A1:A15);B1:B15))
FREQUENCY(A1:A15;A1:A15) gives a 1-column array of 15+1 rows, whereas the second part (B1:B15) is a 1-column array of 15 rows.
I would like to change the resulting array given by FREQUENCY (only in memory -not explicit in sheet-) from a 1-column 16 rows array to a 1-column 15 rows array with the first 15 cell values of that array.
[FREQUENCY documentation: https://support.office.com/en-us/article/FREQUENCY-function-44e3be2b-eca0-42cd-a3f7-fd9ea898fdb9 NB: for Excel, second remark states number of elements that depend on bins_array. ]
I would appreciate suggestions.
Thus, both arrays within MOD will have the same dimensions and SUMPRODUCT will not find cells with error values. I can disregard error values using IF and ISERROR within SUMPRODUCT, but I'd rather disregard the non-relevant part of the FREQUENCY resulting array if it is possible.
It has been thought that making it more specific might be more helpful, so it has been heavily reduced and simplified.

Answer 1

With external help, I have been able to fine-tune a way to solve my problem using INDEX in array formula mode. I am posting the answer in case it helps others.
One way: Put FREQUENCY(A1:A15;A1:A15), or any formula that produces an multi-cell array, within INDEX and have 2nd and/or 3rd arguments as array of consecutive values which will represent rows/columns.
INDEX(FREQUENCY(A1:A15;A1:A15);ROW(INDIRECT("1:" & ROWS(FREQUENCY(A1:A15;A1:A15)-1));1)
First argument within INDEX is the resulting array coming from a formula to shrink (from 16x1 to 15x1), which would be a multi-cell array formula if explicitly entered; second argument is the array 1..15 given by row numbers from 1 to the number of total rows of the "array from formula to shrink" MINUS 1: the first 15 (out of 16) values in the array from a formula; 3rd argument is the column of the shrank array (if need be, more than one could be selected using an analogue to the second argument).
In the particular case of FREQUENCY, because it is known that we are interested in the "bins" part of the function, the formula can be simplified by including the total rows of the "bins"/"intervals" array inside FREQUENCY (its second argument). We will have
INDEX(FREQUENCY(A1:A15;A1:A15);ROW(INDIRECT("1:" & ROWS(A1:A15)));1)
and the complete formula would become
SUMPRODUCT(MOD(INDEX(FREQUENCY(A1:A15;A1:A15);ROW(INDIRECT("1:" & ROWS(A1:A15)));1);B1:B15))
Now, both dividend and divisor of MOD have exactly the same dimensions (15x1) and because B1:B15 includes integers greater than 0 there are no errors.
Thanks all for helping me in making question more concise and better formatted.
ADDITIONAL INFORMATION: As pointed out correctly in comments by XOR LX, this does not seem to work in the widely popular spreadsheet software Excel. It has been developed for an INDEX function inside SUMPRODUCT as used in Open Office Calc which I had mistakenly thought 100% equivalent to Excel's version. A more complete answer perhaps using other functions would be appreciated.

Answer 2

In the previous answer, XOR LX points out very correctly that this formula cannot work in Excel, due to row_num/column_num argument behaviour. Very kindly XOR LX has shown me how that approach can work, and also thanks and credit for supplying a good answer: "INDEX can be used to redimension array (even dynamically created ones) if the row_num/column_num array is coerced to take an arbitrary array with the right dimensions, as shown on this blog entry " The following formula has been checked in Excel 2010 and has the expected results:
SUMPRODUCT(MOD(INDEX(FREQUENCY(A1:A15,A1:A15),N(INDEX(ROW(INDIRECT("1:" & ROWS(A1:A15))),,)),1),B1:B15))
NB: row_num argument of first INDEX, a ROW generated auxiliary array, has been nested inside N(INDEX([...],,)); at least one comma is necessary to account for the two arguments minimum of the nested INDEX. It is in itself interesting the discussion that applies generally to INDEX's arguments, and other functions', that need to be coerced to take arrays (see, here and here at XOR LX's blog). For Open Office users it might be worth stressing the point made at the blog
Unlike OFFSET, (...) for which the first parameter must be a
reference (...) in the worksheet, INDEX can also accept –
and manipulate – for its reference arrays which consist of values
generated e.g. via other subfunctions within the formula. XOR LX's blog
That would be indeed the case in changing the dimension in an array as in this question, but also useful in reversing or displacing the values in an array, for example. Open Office accepts arrays as row_num/column_num, so the coercion is not needed and some formulas rely on this, but without it, these formulas are unlikely to work when files are open in Excel.
Regrettably, this type of coercion is not passed correctly to Open Office, and formula need to be "decoerced" to work, at least in my casual tests.
In order to use a formula that would work in both spreadsheet programs regarding shortening arrays, the only thing I have managed is the following (required: arrays must be single-column)
SUMPRODUCT(
(COLUMN(INDIRECT("R1C1:R"& ROWS(vals_to_mod) &"C"& ROWS(FREQUENCY(vals_for_freq,vals_for_freq)),FALSE))
-ROW(COLUMN(INDIRECT("R1C1:R"& ROWS(vals_to_mod) &"C"& ROWS(FREQUENCY(vals_for_freq,vals_for_freq)),FALSE))
=0)
*MOD(TRANSPOSE(FREQUENCY(vals_for_freq,vals_for_freq)),vals_to_mod)
)
(it "shortens" one array to the shortest of the pair, by creating an auxiliary array with TRUE/1s on the diagonal starting top-left and FALSE/0s elsewhere, therefore disregarding all defined values outside the square section of the array. Thus, SUMPRODUCT adds values within the diagonal of the square section which are the product of the corresponding values up to the last value of the shorter array.)