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

1,6

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

Links

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

Formula

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A048250, A325313, A325385.

Sequence in context: A323166 A007732 A237835 * A348929 A334491 A276997

Adjacent sequences: A126792 A126793 A126794 * A126796 A126797 A126798

Keyword

nonn

Author

Leroy Quet, Mar 14 2007

Extensions

More terms from Emeric Deutsch, Mar 27 2007

Status

approved