A376882 a(n) is the product of the Zumkeller divisors of n.

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

Comments

d is a Zumkeller divisor of n if and only if d is a divisor of n and is Zumkeller (A083207).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

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);

Prog

(PARI) A376882(n) = { my(m=1); fordiv(n, d, if(A083206(d)>0, m *= d)); (m); }; \\ Antti Karttunen, Dec 02 2024

Crossrefs

Cf. A083207, A023196, A171641, A376880 (positions of terms > 1).

Sequence in context: A167155 A369465 A268731 * A080219 A339747 A293901

Adjacent sequences: A376879 A376880 A376881 * A376883 A376884 A376885

Keyword

nonn

Author

Peter Luschny, Oct 19 2024

Status

approved