A308098 - OEIS

%I #20 Sep 08 2022 08:46:21

%S 1,2,3,5,4,7,9,13,8,19,12,29,22,37,18,27,43,49,61,32,67,73,45,36,50,

%T 101,109,91,81,64,121,137,149,157,133,106,163,98,173,129,169,193,72,

%U 197,199,134,211,100,146,229,241,128,217,257,171,148,277,281,283,219

%N Numbers m such that sequence of their values of sigma(m) corresponds to sequence of unique values of function sigma(n) for n >= 1 in increasing order (A007370).

%C A211656 is the sorted version of this sequence.

%H Amiram Eldar, <a href="/A308098/b308098.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F A000203(a(n)) = A007370(n) for all n.

%e a(6) = 7 because A007370(6) = 8 and there is only one solution of equation sigma(x) = 8 for x = 7.

%t m = 500; v = Table[0, {m}]; Do[s = DivisorSigma[1, k]; If[s <= m ,  v[[s]] = If[ v[[s]] == 0, k, -1]], {k, 1, m - 1}]; Select[v, # > 0 &] (* _Amiram Eldar_, Jul 04 2019 *)

%o (Magma) [[m: m in [1..1000] | SumOfDivisors(m) eq n]:  n in [1..100] | #[#[m]: m in [1..1000] | SumOfDivisors(m) eq n] eq 1]

%Y Cf. A000203, A007370, A211656, A211657.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, May 12 2019