This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376880 #25 Dec 02 2024 17:07:34
%S A376880 6,12,18,20,24,28,30,36,40,42,48,54,56,60,66,70,72,78,80,84,88,90,96,
%T A376880 100,102,104,108,112,114,120,126,132,138,140,144,150,156,160,162,168,
%U A376880 174,176,180,186,192,196,198,200,204,208,210,216,220,222,224,228,234,240,246,252,258,260,264,270
%N A376880 Numbers that have Zumkeller divisors.
%C A376880 d is a Zumkeller divisor of n if and only if d is a divisor of n and is Zumkeller (A083207).
%C A376880 The first difference from A023196 is 748, which is abundant (sigma(748) = 1512 > 2*748) but has no Zumkeller divisors.
%H A376880 Peter Luschny, <a href="/A376880/b376880.txt">Table of n, a(n) for n = 1..10000</a>
%e A376880 The Zumkeller divisors of 80 are {20, 40, 80}, so 80 is a term.
%e A376880 The divisors of 81 are {1, 3, 9, 27, 81}, none of which is Zumkeller, so 81 is not a term.
%p A376880 with(NumberTheory):
%p A376880 isZumkeller := proc(n) option remember; local s, p, i, P;
%p A376880 s := SumOfDivisors(n);
%p A376880 if s::odd or s < n*2 then false else
%p A376880 P := mul(1 + x^i, i in Divisors(n));
%p A376880 is(0 < coeff(P, x, s/2)) fi end:
%p A376880 select(n -> ormap(isZumkeller, Divisors(n)), [seq(1..270)]);
%t A376880 znQ[n_]:=Length[Select[{#, Complement[Divisors[n], #]}&/@Most[Rest[ Subsets[ Divisors[ n]]]], Total[#[[1]]]==Total[#[[2]]]&]]>0; zn=Select[Range[300], znQ] (* zn from A083207 *) ;Select[Range[270],IntersectingQ[Divisors[#],zn]&] (* _James C. McMahon_, Oct 23 2024 *)
%Y A376880 Cf. A083207, A023196, A171641, A376879, A376881.
%Y A376880 Positions of terms > 1 in A376882, terms > 0 in A378446.
%K A376880 nonn
%O A376880 1,1
%A A376880 _Peter Luschny_, Oct 20 2024
%E A376880 Incorrect comment removed by _Peter Luschny_, Dec 02 2024