cp's OEIS Frontend

A249421 A(n,k) = exponent of the largest power of n-th prime which divides the product of the elements on row (k-1) of Pascal's triangle; a square array read by antidiagonals.

%I A249421 #22 Sep 20 2016 13:26:01
%S A249421 0,0,0,1,0,0,0,0,0,0,5,2,0,0,0,2,1,0,0,0,0,4,0,0,0,0,0,0,0,4,4,0,0,0,
%T A249421 0,0,17,2,3,0,0,0,0,0,0,10,0,2,0,0,0,0,0,0,0,12,14,1,6,0,0,0,0,0,0,0,
%U A249421 4,10,0,5,0,0,0,0,0,0,0,0,18,6,8,4,0,0,0,0,0,0,0,0,0,8,13,6,3,0,0,0,0,0,0,0,0,0,0,11,8,4,2,0,0,0,0,0,0,0,0,0,0,0
%N A249421 A(n,k) = exponent of the largest power of n-th prime which divides the product of the elements on row (k-1) of Pascal's triangle; a square array read by antidiagonals.
%C A249421 Square array A(n,k), where n = row, k = column, read by antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ....
%C A249421 A(n,k) is A000040(n)-adic valuation of A001142(k-1).
%H A249421 Jeffrey C. Lagarias, Harsh Mehta, <a href="http://arxiv.org/abs/1409.4145">Products of binomial coefficients and unreduced Farey fractions</a>, arXiv:1409.4145 [math.NT], 2014.
%F A249421 A(n, k) = A249344(n, A001142(k-1)).
%e A249421 The top left corner of the array:
%e A249421 0, 0, 1, 0, 5, 2, 4, 0, 17, 10, 12,  4, 18,  8, 11,  0, 49, 34, 36, 20, 42,
%e A249421 0, 0, 0, 2, 1, 0, 4, 2,  0, 14, 10,  6, 13,  8,  3, 12,  6,  0, 28, 20, 12,
%e A249421 0, 0, 0, 0, 0, 4, 3, 2,  1,  0,  8,  6,  4,  2,  0, 12,  9,  6,  3,  0, 16,
%e A249421 0, 0, 0, 0, 0, 0, 0, 6,  5,  4,  3,  2,  1,  0, 12, 10,  8,  6,  4,  2,  0,
%e A249421 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0, 10,  9,  8,  7,  6,  5,  4,  3,  2,  1,
%e A249421 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0, 12, 11, 10,  9,  8,  7,  6,  5,
%e A249421 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 16, 15, 14, 13,
%e A249421 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18, 17,
%e A249421 ...
%o A249421 (Scheme)
%o A249421 (define (A249421 n) (A249421bi (A002260 n) (A004736 n)))
%o A249421 (define (A249421bi row col) (A249344bi row (A001142 (- col 1)))) ;; Code for A249344bi given in A249344.
%Y A249421 Transpose: A249422.
%Y A249421 Row 1: A187059, Row 2: A249343, Row 3: A249345, Row 4 A249347. (Cf. also A249346).
%Y A249421 Cf. A000040, A001142, A007318, A249344, A249151.
%K A249421 nonn,tabl
%O A249421 1,11
%A A249421 _Antti Karttunen_, Oct 28 2014