A376882 - OEIS

%I #17 Dec 02 2024 07:22:28

%S 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,

%T 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,

%U 1,1,2592000,1,1,1,1,1,396,1,1,1,70,1,1728,1,1,1,1,1,468,1,64000

%N a(n) is the product of the Zumkeller divisors of n.

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

%H Antti Karttunen, <a href="/A376882/b376882.txt">Table of n, a(n) for n = 1..10000</a>

%e The Zumkeller divisors of 80 are {20, 40, 80}, so a(80) = 64000.

%e The divisors of 81 are {1, 3, 9, 27, 81}, none of which is Zumkeller, so a(81) = 1.

%p # The function 'isZumkeller' is defined in A376880.

%p with(NumberTheory):

%p zdiv := n -> select(isZumkeller, Divisors(n));

%p a := n -> mul(k, k in zdiv(n));

%p seq(a(n), n = 1..80);

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

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

%K nonn

%O 1,6

%A _Peter Luschny_, Oct 19 2024