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
KEYWORD
AUTHOR
Enoch Haga, Feb 20 2000
EXTENSIONS
Missing term a(9)=17 is added by Zak Seidov, Sep 11 2009
STATUS
approved