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A053728 For n=1,2,3,..., compute sum of aliquot divisors of n; if result is prime append this prime to sequence. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A206945 A206946 A059055

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

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Last modified August 10 22:22 EDT 2020. Contains 336403 sequences. (Running on oeis4.)