%I #19 Sep 08 2022 08:46:16

%S 2,11,16,19,22,23,25,27,29,34,35,37,41,43,45,46,47,49,51,52,53,55,58,

%T 59,61,64,66,67,69,70,71,75,76,77,79,81,83,86,87,88,89,92,94,95,97,99,

%U 100,101,103,105,106,107,109,111,113,115,116,117,118,119,123,125

%N Numbers n such that sigma_k(x) = n has no solution for any k > 0.

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

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

%C Complement of A211347.

%C Numbers n such that A271606(n) = 0.

%H Amiram Eldar, <a href="/A272883/b272883.txt">Table of n, a(n) for n = 1..10000</a>

%o (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]))]

%Y 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).

%Y Cf. A211347, A271606.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, May 08 2016