A272883 Numbers m such that sigma_k(x) = m has no solution for any k > 0.

2, 11, 16, 19, 22, 23, 25, 27, 29, 34, 35, 37, 41, 43, 45, 46, 47, 49, 51, 52, 53, 55, 58, 59, 61, 64, 66, 67, 69, 70, 71, 75, 76, 77, 79, 81, 83, 86, 87, 88, 89, 92, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 109, 111, 113, 115, 116, 117, 118, 119, 123, 125

Offset: 1

Author

Jaroslav Krizek, May 08 2016

Keywords

• nonn

Comments

Recall that sigma_k(n) = Sum_{d|n} d^k.

Sigma_0(n), the number of divisors of n, can be any positive integer and so is ignored in this sequence.

Complement of A211347.

Numbers n such that A271606(n) = 0.

Links

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

Crossrefs

Cf. Sequences of sigma_k(n) for k=0-24: A000005 (k=0), A000203 (k=1), A001157-A001160 (k=2-5), A013954-A013972 (k=6-24).

Cf. A211347, A271606.

Programs

Magma

[n: n in [1..2^7] | [n] notsubset Set(Sort([DivisorSigma(k,n): n in [1..2^7+1], k in [1..2^7+1] | DivisorSigma(k,n) lt 2^7+1]))];