A368092 - OEIS

A368092

a(n) = A160014(m, n) * a(n - 1) for m = 2 and n > 0, a(0) = 1.

1, 3, 9, 135, 405, 8505, 127575, 382725, 1148175, 189448875, 3978426375, 155158628625, 2327379429375, 6982138288125, 20946414864375, 37389350532909375, 112168051598728125, 6393578941127503125, 1054940525286038015625, 3164821575858114046875, 66461253093020394984375

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OFFSET

0,2

COMMENTS

A160014 are the generalized Clausen numbers. For m = 0 the formula computes the cumulative radical A048803, for m = 1 the Hirzebruch numbers A091137.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) = 2^(n mod 2 - n)*lcm_{p in Partitions(n)} (Product_{t in p}(t + 2)).

a(n) = 2^(n mod 2 - n)*A368048(n).

a(n) = A368117(n) * a(n-1) for n > 0.

PROG

(SageMath)

from functools import cache

@cache

def a_rec(n):

if n == 0: return 1

p = mul(s for s in map(lambda i: i + 2, divisors(n)) if is_prime(s))

return p * a_rec(n - 1)

print([a_rec(n) for n in range(21)])

# Alternatively, but less efficient:

def a(n): return (2**(n%2 - n) * lcm(product(r + 2 for r in p) for p in Partitions(n)))

CROSSREFS

Cf. A160014, A048803 (m=0), A091137 (m=1), this sequence (m=2), A368093 (array), A368048, A368117.

Sequence in context: A289169 A257032 A141143 * A163402 A288757 A289900

Adjacent sequences: A368089 A368090 A368091 * A368093 A368094 A368095

KEYWORD

nonn

AUTHOR

Peter Luschny, Dec 12 2023

STATUS

approved