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A368093
Cumulative products of the generalized Clausen numbers. Array read by ascending antidiagonals.
2
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, 360, 1, 7, 7, 875, 175, 8505, 60480, 2520, 1, 1, 49, 7, 4375, 175, 127575, 120960, 5040, 1, 1, 1, 343, 49, 21875, 875, 382725, 3628800, 15120
OFFSET
0,5
COMMENTS
A160014 are the generalized Clausen numbers, for m = 0 the formula computes the cumulative radical A048803, and for m = 1 the Hirzebruch numbers A091137.
FORMULA
A(m, n) = A160014(m, n) * A(m, n - 1) for n > 0 and A(m, 0) = 1.
EXAMPLE
Array A(m, n) starts:
[0] 1, 1, 2, 6, 12, 60, 360, 2520, ... A048803
[1] 1, 2, 12, 24, 720, 1440, 60480, 120960, ... A091137
[2] 1, 3, 9, 135, 405, 8505, 127575, 382725, ... A368092
[3] 1, 1, 5, 5, 175, 175, 875, 875, ...
[4] 1, 5, 25, 875, 4375, 21875, 765625, 42109375, ...
[5] 1, 1, 7, 7, 49, 49, 3773, 3773, ...
[6] 1, 7, 49, 343, 2401, 184877, 1294139, 117766649, ...
[7] 1, 1, 1, 1, 11, 11, 143, 143, ...
[8] 1, 1, 1, 11, 11, 143, 1573, 1573, ...
[9] 1, 1, 11, 11, 1573, 1573, 17303, 17303, ...
PROG
(SageMath)
from functools import cache
def Clausen(n, k):
return mul(s for s in map(lambda i: i+n, divisors(k)) if is_prime(s))
@cache
def CumProdClausen(m, n):
return Clausen(m, n) * CumProdClausen(m, n - 1) if n > 0 else 1
for m in range(10): print([m], [CumProdClausen(m, n) for n in range(8)])
CROSSREFS
Cf. A160014, A048803 (m=0), A091137 (m=1), A368092 (m=2).
Sequence in context: A258222 A112324 A061531 * A368116 A338435 A214722
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Dec 12 2023
STATUS
approved