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A376882
a(n) is the product of the Zumkeller divisors of n (d is a Zumkeller divisor of n if and only if d is a divisor of n and is Zumkeller (A083207)).
2
1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 72, 1, 1, 1, 1, 1, 6, 1, 20, 1, 1, 1, 1728, 1, 1, 1, 28, 1, 180, 1, 1, 1, 1, 1, 72, 1, 1, 1, 800, 1, 252, 1, 1, 1, 1, 1, 82944, 1, 1, 1, 1, 1, 324, 1, 1568, 1, 1, 1, 2592000, 1, 1, 1, 1, 1, 396, 1, 1, 1, 70, 1, 1728, 1, 1, 1, 1, 1, 468, 1, 64000
OFFSET
1,6
EXAMPLE
The Zumkeller divisors of 80 are {20, 40, 80}, so a(80) = 64000.
The divisors of 81 are {1, 3, 9, 27, 81}, none of which is Zumkeller, so a(81) = 1.
MAPLE
# The function 'isZumkeller' is defined in A376880.
with(NumberTheory):
zdiv := n -> select(isZumkeller, Divisors(n));
a := n -> mul(k, k in zdiv(n));
seq(a(n), n = 1..80);
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Oct 19 2024
STATUS
approved