A243765 Numbers that have all their divisors in A002191 (possible values for sigma(n), A000203).

1, 3, 7, 13, 31, 39, 91, 93, 127, 217, 307, 381, 403, 921, 961, 1093, 1209, 1651, 1723, 2149, 2801, 2821, 3279, 3541, 3937, 3991, 4953, 5113, 5169, 7651, 8011, 8191, 8403, 9517, 10303, 10623, 11811, 11973, 12061, 12493, 15339, 17293, 19531, 19607, 22399

Offset: 1

Author

Michel Marcus, Jun 10 2014

Keywords

• nonn

Comments

Since 2 does not belong to A002191, all terms are odd.

All primes p that are in A023195 (Prime numbers that are the sum of the divisors of some n), are also in this sequence; and the prime factors of all terms can only belong to A023195.

Up to 10^7, only one term is a prime power: 961=31^2 (being a square, see A038688, A228061 and A243810).

Examples

			The divisors of 3 are 1 and 3 that both belong to A002191, 1 as sigma(1) and 3 as sigma(2).
The divisors of 39 are 1, 3, 13 and 39 all of which belong to A002191, 13 as sigma(9) 39 as sigma(18).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000203, A002191, A023195.

Cf. A045572 (analog sequence with the sum of proper divisors instead).

Programs

Maple

N:= 10^6: # to get all terms up to N
A002191:= select(`<=`,{seq(numtheory[sigma](i),i=1..N)},N):
A243765:= select(t -> numtheory[divisors](t) subset A002191, A002191); # Robert Israel, Jun 16 2014

PARI

list(lim) = select(n->n<=lim, Set(vector(lim\=1, n, sigma(n))));
isok(n, lists) = {fordiv (n, d, if (!vecsearch(lists, d), return(0))); return(1);}
lista(nn) = {lists = list(nn); for(n=1, nn, if (isok(n, lists), print1(n, ", ")););}