A099636 - OEIS

A099636

a(n) = gcd(sum of distinct prime factors of n, product of distinct prime factors of n).

1, 2, 3, 2, 5, 1, 7, 2, 3, 1, 11, 1, 13, 1, 1, 2, 17, 1, 19, 1, 1, 1, 23, 1, 5, 1, 3, 1, 29, 10, 31, 2, 1, 1, 1, 1, 37, 1, 1, 1, 41, 6, 43, 1, 1, 1, 47, 1, 7, 1, 1, 1, 53, 1, 1, 1, 1, 1, 59, 10, 61, 1, 1, 2, 1, 2, 67, 1, 1, 14, 71, 1, 73, 1, 1, 1, 1, 6, 79, 1, 3, 1, 83, 6, 1, 1, 1, 1, 89, 10, 1, 1, 1

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

FORMULA

From Antti Karttunen, Feb 01 2021: (Start)

a(n) = gcd(A007947(n), A008472(n)).

a(n) = A007947(n) / A340677(n) = A008472(n) / A340678(n).

(End)

EXAMPLE

n=84: a(84) = gcd(2*3*7, 2+3+7) = gcd(42, 12) = 6.

MATHEMATICA

PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; f[n_] := Block[{pf = PrimeFactors[n]}, GCD[Plus @@ pf, Times @@ pf]]; Table[ f[n], {n, 93}] (* Robert G. Wilson v, Nov 04 2004 *)

PROG

(PARI)

A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947

A008472(n) = vecsum(factor(n)[, 1]); \\ From A008472

A099636(n) = gcd(A007947(n), A008472(n));

CROSSREFS

Cf. A007947, A008472, A082299, A099634, A340677, A340678.

Differs from related A099635 for the first time at n=84, where a(84) = 6, while A099635(84) = 12.

Differs from A014963 for the first time at n=30, where a(30) = 10, while A014963(30) = 1.

Sequence in context: A157753 A020500 A014963 * A099635 A178380 A178375

Adjacent sequences: A099633 A099634 A099635 * A099637 A099638 A099639

KEYWORD

nonn

AUTHOR

Labos Elemer, Oct 28 2004

EXTENSIONS

Name clarified by Antti Karttunen, Feb 01 2021

STATUS

approved