A320515 Squarefree k > 1 with sigma(sigma(k)) < 2*k + 1.

2, 13, 37, 43, 61, 67, 73, 97, 109, 151, 157, 163, 181, 193, 211, 229, 241, 277, 283, 313, 331, 337, 373, 397, 409, 421, 433, 457, 487, 523, 541, 547, 577, 601, 613, 631, 661, 673, 691, 709, 733, 751, 757, 787, 823, 829, 853, 877, 883, 907, 937, 997

Offset: 1

Author

Peter Luschny, Oct 14 2018

Keywords

• nonn

Comments

Conjecturally a subsequence of A085497.

This conjecture is false, the first counterexample is a(113) = 2257 = 37 * 61 which is the least composite term in this sequence. - Amiram Eldar, Jun 17 2020

Links

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

Crossrefs

Cf. A085497, A000668.

Programs

Maple

isA320515 := n -> (n > 1) and issqrfree(n) and (sigma(sigma(n)) < 2*n+1):
select(isA320515, [$1..1000]);

Mathematica

Rest[Select[Range[1000], SquareFreeQ[#] && DivisorSigma[1, DivisorSigma[1, #]] < 2*# + 1 &]] (* Vaclav Kotesovec, Oct 14 2018 *)

PARI

isok(n) = (n>1) && issquarefree(n) && (sigma(sigma(n)) < 2*n + 1); \\ Michel Marcus, Oct 14 2018