This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A368093 #9 Dec 14 2023 16:28:33 %S A368093 1,1,1,1,2,2,1,3,12,6,1,1,9,24,12,1,5,5,135,720,60,1,1,25,5,405,1440, %T A368093 360,1,7,7,875,175,8505,60480,2520,1,1,49,7,4375,175,127575,120960, %U A368093 5040,1,1,1,343,49,21875,875,382725,3628800,15120 %N A368093 Cumulative products of the generalized Clausen numbers. Array read by ascending antidiagonals. %C A368093 A160014 are the generalized Clausen numbers, for m = 0 the formula computes the cumulative radical A048803, and for m = 1 the Hirzebruch numbers A091137. %F A368093 A(m, n) = A160014(m, n) * A(m, n - 1) for n > 0 and A(m, 0) = 1. %e A368093 Array A(m, n) starts: %e A368093 [0] 1, 1, 2, 6, 12, 60, 360, 2520, ... A048803 %e A368093 [1] 1, 2, 12, 24, 720, 1440, 60480, 120960, ... A091137 %e A368093 [2] 1, 3, 9, 135, 405, 8505, 127575, 382725, ... A368092 %e A368093 [3] 1, 1, 5, 5, 175, 175, 875, 875, ... %e A368093 [4] 1, 5, 25, 875, 4375, 21875, 765625, 42109375, ... %e A368093 [5] 1, 1, 7, 7, 49, 49, 3773, 3773, ... %e A368093 [6] 1, 7, 49, 343, 2401, 184877, 1294139, 117766649, ... %e A368093 [7] 1, 1, 1, 1, 11, 11, 143, 143, ... %e A368093 [8] 1, 1, 1, 11, 11, 143, 1573, 1573, ... %e A368093 [9] 1, 1, 11, 11, 1573, 1573, 17303, 17303, ... %o A368093 (SageMath) %o A368093 from functools import cache %o A368093 def Clausen(n, k): %o A368093 return mul(s for s in map(lambda i: i+n, divisors(k)) if is_prime(s)) %o A368093 @cache %o A368093 def CumProdClausen(m, n): %o A368093 return Clausen(m, n) * CumProdClausen(m, n - 1) if n > 0 else 1 %o A368093 for m in range(10): print([m], [CumProdClausen(m, n) for n in range(8)]) %Y A368093 Cf. A160014, A048803 (m=0), A091137 (m=1), A368092 (m=2). %Y A368093 Cf. A171080, A238963, A368116, A368048. %K A368093 nonn,tabl %O A368093 0,5 %A A368093 _Peter Luschny_, Dec 12 2023