A337399 Numbers k such that sigma(k) is a Zumkeller number (A083207).

5, 6, 11, 12, 14, 15, 19, 20, 23, 24, 26, 27, 28, 29, 33, 34, 35, 38, 39, 40, 41, 42, 44, 45, 47, 53, 54, 56, 57, 58, 59, 60, 62, 63, 65, 68, 69, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 95, 96, 99, 101, 102, 103

Offset: 1

Author

Ivan N. Ianakiev, Aug 26 2020

Keywords

• nonn
• easy

Comments

Sequence contains many semiprimes of the form p(m)*p(m+1). Only 6 of the first 200 semiprimes of this form are not terms, those where m is in {15, 37, 99, 100, 121, 197}.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A083207, A320518 (subsequence).

Programs

Mathematica

zQ[n_]:=Module[{d=Divisors[n],t,ds,x},ds=Plus@@d;If[Mod[ds,2]>0,False,t=CoefficientList[Product[1+x^i,{i,d}],x];t[[1+ds/2]]>0]]; Select[Range[200],zQ[DivisorSigma[1,#]]&] (* code by T. D. Noe at A083207 *)