A308098 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).

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, 101, 109, 91, 81, 64, 121, 137, 149, 157, 133, 106, 163, 98, 173, 129, 169, 193, 72, 197, 199, 134, 211, 100, 146, 229, 241, 128, 217, 257, 171, 148, 277, 281, 283, 219

Offset: 1

Author

Jaroslav Krizek, May 12 2019

Keywords

• nonn

Comments

A211656 is the sorted version of this sequence.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A007370, A211656, A211657.

Programs

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]

Mathematica

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 *)

Formula

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