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A126795 a(n) = gcd(n, Product_{p|n} (p+1)), where the product is over the distinct primes p that divide n. 5
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 (list; graph; refs; listen; history; text; internal format)
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 * A334491 A276997 A324394

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

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)