A126864 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, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 5, 2, 3, 2, 1, 4, 1, 2, 3, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 4, 1, 2, 1, 12, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 3

Offset: 1

Author

Leroy Quet, Mar 15 2007

Keywords

• nonn

Comments

Product_{p|n} (p-1) is the absolute value of A023900(n) (that is, A173557(n)).

First occurrence of k: 1, 6, 21, 20, 55, 42, 203, 120, 171, 110, 253, 84, 689, 406, 465, 272, 1751, 342, 3629, 220, ..., . - Robert G. Wilson v

Examples

			The distinct primes that divide 20 are 2 and 5. So a(20) = gcd(20, (2-1)(5-1)) = gcd(20,4) = 4.
		

Links

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

Crossrefs

Cf. A000010, A023900, A173557, A318841, A319341.

Programs

Maple

with(numtheory): a:=n->gcd(n,product(factorset(n)[i]-1,i=1..nops(factorset(n)))); # Emeric Deutsch, Apr 11 2007

Mathematica

f[n_] := GCD[n, Times @@ (First /@ FactorInteger[n] - 1)]; Array[f, 105] (* Robert G. Wilson v, Sep 08 2007 *)

PARI

A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
A126864(n) = gcd(n, A173557(n)); \\ Antti Karttunen, Sep 17 2018

Formula

a(n) = gcd(n, A173557(n)) = gcd(n, A318841(n)). - Antti Karttunen, Sep 17 2018

Extensions

More terms from Emeric Deutsch, Apr 11 2007