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

Offset: 1

Author

Labos Elemer, Oct 28 2004

Keywords

• nonn

Examples

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

Links

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

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.

Programs

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 *)

PARI

A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
A008472(n) = vecsum(factor(n)[, 1]); \\ From A008472
A099636(n) = gcd(A007947(n), A008472(n));

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)

Extensions

Name clarified by Antti Karttunen, Feb 01 2021