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

1,6

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

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A247371 A331177 A173751 * A348928 A124766 A359233

Adjacent sequences: A126861 A126862 A126863 * A126865 A126866 A126867

Keyword

nonn

Author

Leroy Quet, Mar 15 2007

Extensions

More terms from Emeric Deutsch, Apr 11 2007

Status

approved