A162923 Numbers k such that the equation sigma(sigma(x)) = k has no solutions.

2, 3, 5, 6, 9, 10, 11, 13, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 36, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 92, 93

Offset: 1

Author

Jaroslav Krizek, Jul 17 2009

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Complement of A070286.

Cf. A051027.

Programs

Mathematica

mx = 100; Complement[Range[mx], Table[Nest[DivisorSigma[1, #] &, n, 2], {n, mx}]] (* Ivan Neretin, Feb 12 2018 *)

PARI

is(k) = {my(v = invsigma(k)); for(i = 1, #v, if(invsigmaNum(v[i]) > 0, return(0))); 1;} \\ Amiram Eldar, Dec 26 2024, using Max Alekseyev's invphi.gp

Formula

{A000027} minus {A070286}.