A368093 - OEIS

%I #9 Dec 14 2023 16:28:33

%S 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 360,1,7,7,875,175,8505,60480,2520,1,1,49,7,4375,175,127575,120960,

%U 5040,1,1,1,343,49,21875,875,382725,3628800,15120

%N Cumulative products of the generalized Clausen numbers. Array read by ascending antidiagonals.

%C 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 A(m, n) = A160014(m, n) * A(m, n - 1) for n > 0 and A(m, 0) = 1.

%e Array A(m, n) starts:

%e   [0] 1, 1,  2,   6,   12,     60,     360,      2520, ...  A048803

%e   [1] 1, 2, 12,  24,  720,   1440,   60480,    120960, ...  A091137

%e   [2] 1, 3,  9, 135,  405,   8505,  127575,    382725, ...  A368092

%e   [3] 1, 1,  5,   5,  175,    175,     875,       875, ...

%e   [4] 1, 5, 25, 875, 4375,  21875,  765625,  42109375, ...

%e   [5] 1, 1,  7,   7,   49,     49,    3773,      3773, ...

%e   [6] 1, 7, 49, 343, 2401, 184877, 1294139, 117766649, ...

%e   [7] 1, 1,  1,   1,   11,     11,     143,       143, ...

%e   [8] 1, 1,  1,  11,   11,    143,    1573,      1573, ...

%e   [9] 1, 1, 11,  11, 1573,   1573,   17303,     17303, ...

%o (SageMath)

%o from functools import cache

%o def Clausen(n, k):

%o     return mul(s for s in map(lambda i: i+n, divisors(k)) if is_prime(s))

%o @cache

%o def CumProdClausen(m, n):

%o     return Clausen(m, n) * CumProdClausen(m, n - 1) if n > 0 else 1

%o for m in range(10): print([m], [CumProdClausen(m, n) for n in range(8)])

%Y Cf. A160014, A048803 (m=0), A091137 (m=1), A368092 (m=2).

%Y Cf. A171080, A238963, A368116, A368048.

%K nonn,tabl

%O 0,5

%A _Peter Luschny_, Dec 12 2023