

A309727


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


1



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
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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 A108053 A327969
Adjacent sequences: A309724 A309725 A309726 * A309728 A309729 A309730


KEYWORD

nonn


AUTHOR

Michel Marcus, Oct 14 2019


STATUS

approved



