A126795 a(n) = gcd(n, Product_{p|n} (p+1)), where the product is over the distinct primes p that divide n.

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 12, 1, 2, 3, 1, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 1, 12, 1, 2, 1, 2, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 3, 4, 1, 18, 7, 4, 1, 2, 5, 12, 1, 2, 3, 2, 1

Offset: 1

Author

Leroy Quet, Mar 14 2007

Keywords

• nonn

Comments

First occurrence of k: 1, 10, 15, 28, 95, 6, 91, 56, 153, 190, 473, 12, 1339, 182, 285, 496, 1139, 90, 703, 380, ..., . - Robert G. Wilson v

Examples

			The distinct primes that divide 28 are 2 and 7. So a(28) = GCD(28, (2+1)(7+1)) = GCD(28, 24) = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A048250, A325313, A325385.

Programs

Maple

with(numtheory): a:=proc(n) local fs: fs:=factorset(n): gcd(n,product(1+fs[i],i=1..nops(fs))) end: seq(a(n),n=1..120); # Emeric Deutsch, Mar 27 2007

Mathematica

f[n_] := GCD[n, Times @@ (First /@ FactorInteger[n] + 1)]; Array[f, 101] (* Robert G. Wilson v *)

PARI

A126795(n) = gcd(n,factorback(apply(p -> p+1,factor(n)[,1]))); \\ Antti Karttunen, Sep 10 2018

Formula

a(n) = gcd(n, A048250(n)).

a(n) = gcd(n, A325313(n)) = gcd(n, A048250(n)-n). - Antti Karttunen, Apr 24 2019

Extensions

More terms from Emeric Deutsch, Mar 27 2007