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A126864 a(n) = gcd(n, Product_{p|n} (p-1)), where the product is over the distinct primes, p, that divide n. 3
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 (list; graph; refs; listen; history; text; internal format)
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 * A124766 A337323 A293895

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

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Last modified May 9 09:27 EDT 2021. Contains 343699 sequences. (Running on oeis4.)