A309727 a(n) is the least integer k such that for some iteration of sigma applied to k, one gets the n-th term of A002191, the list of possible values for the function sum of divisors.

1, 2, 2, 5, 2, 2, 5, 9, 9, 2, 10, 19, 2, 5, 29, 16, 16, 22, 37, 10, 27, 19, 43, 33, 34, 5, 49, 2, 61, 16, 67, 29, 73, 45, 49, 43, 27, 22, 50, 19, 52, 101, 16, 85, 109, 22, 73, 5, 81, 33, 67, 64, 50, 86, 81, 137, 76, 66, 149, 111, 99, 157, 81, 106, 163, 2, 52, 173, 129

Offset: 1

Author

Michel Marcus, Oct 14 2019

Keywords

• nonn

Comments

The set union of this sequence is 1 U A007369.

Examples

			For n = 5, A002191(5) is 7, and 4 iterations of sigma applied to 2 give 7, and no integer less than 2 will give 7, so a(5)=2.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..2503

Crossrefs

Cf. A000203, A002191, A007369, A007497, A051572, A257349.

A257670 is a better version for this sequence.

Programs

PARI

list(lim) = select(n->n<=lim, Set(vector(lim\=1, n, sigma(n))));
lista(nn) = {my(vs = list(nn), v = vector(#vs)); v[1] = 1; for (n=2, #vs, for (k=2, vs[n], my(kk=k); while (sigma(kk) <= vs[n], kk=sigma(kk)); if (kk == vs[n], v[n] = k; break););); v;}

Formula

a(n) = 2 when A002191(n) is in A007497.

a(n) = 5 when A002191(n) is in A051572.

a(n) = 16 when A002191(n) is in A257349.