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

1,2

Comments

The set union of this sequence is 1 U A007369.

Links

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

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.

Example

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.

Prog

(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; }

Crossrefs

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

A257670 is a better version for this sequence.

Sequence in context: A229709 A242277 A241476 * A195719 A327969 A328324

Adjacent sequences: A309724 A309725 A309726 * A309728 A309729 A309730

Keyword

nonn

Author

Michel Marcus, Oct 14 2019

Status

approved