A376881 Numbers that have exactly one Zumkeller divisor.

6, 18, 20, 28, 70, 88, 100, 104, 196, 272, 304, 368, 464, 496, 550, 572, 650, 836, 945, 968, 1184, 1312, 1352, 1376, 1430, 1504, 1575, 1696, 1870, 1888, 1952, 2002, 2090, 2205, 2210, 2470, 2530, 2584, 2990, 3128, 3190, 3230, 3410, 3465, 3496, 3770, 3944

Offset: 1

Author

Peter Luschny, Oct 19 2024

Keywords

• nonn

Comments

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

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A376880.

Cf. A083207, A376877, A376882, A023196, A171641.

Programs

Maple

# The function 'isZumkeller' is defined in A376880.
zdiv := n -> select(isZumkeller, NumberTheory:-Divisors(n)):
select(n -> nops(zdiv(n)) = 1, [seq(1..4000)]);

Formula

If d is the only Zumkeller divisor of n and n is Zumkeller then d = n.