A053728 For n=1,2,3,..., compute sum of aliquot divisors of n; if result is prime append this prime to sequence.

3, 7, 11, 13, 31, 13, 17, 43, 17, 23, 41, 19, 19, 23, 73, 41, 29, 31, 127, 47, 37, 31, 89, 73, 43, 29, 131, 71, 37, 47, 31, 31, 53, 83, 157, 97, 59, 97, 137, 101, 37, 67, 107, 41, 37, 523, 109, 113, 73, 211, 43, 79, 61, 43, 131, 191, 41, 463, 241, 67, 89, 43, 53, 103, 167

Offset

1,1

Comments

Intersection of A001065 and the primes. - Michel Marcus, Jun 06 2014

From Robert Israel, Mar 26 2018: (Start)

If p is a prime > 7, a slightly stronger form of the Goldbach conjecture implies there are two distinct primes q,r such that p-1=q+r. Then sigma(q*r)-q*r=q+r+1=p. Thus every prime > 7 should appear at least once in this sequence. The primes 3=a(1) and 7=a(2) also appear, but 2 and 5 do not.

If n is composite, A001065(n) > sqrt(n). Thus a(n) -> infinity as n -> infinity. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(4)=13 because when n=27, divisors are 1, 3, 9, which sum to 13, prime.

Maple

select(isprime, [seq(numtheory:-sigma(n)-n, n=1..1000)]); # Robert Israel, Mar 26 2018

Mathematica

Table[If[PrimeQ[DivisorSigma[1, n]-n], DivisorSigma[1, n]-n, {}], {n, 1000}]//Flatten (* Harvey P. Dale, Jul 16 2016 *)

Prog

(PARI) lsadp(nn) = {for (n=1, nn, sad = sigma(n) - n; if (isprime(sad), print1(sad, ", ")); ); } \\ Michel Marcus, Jun 06 2014

Crossrefs

Cf. A001065.

Sequence in context: A086475 A154832 A164568 * A342183 A206945 A206946

Adjacent sequences: A053725 A053726 A053727 * A053729 A053730 A053731

Keyword

easy,nonn,look

Author

Enoch Haga, Feb 20 2000

Extensions

Missing term a(9)=17 is added by Zak Seidov, Sep 11 2009

Status

approved