A099635 a(n) = gcd(sum of all prime factors of n, 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, 12, 1, 1, 1, 1, 89, 10, 1, 1, 1

Offset: 1

Author

Labos Elemer, Oct 28 2004

Keywords

• nonn

Comments

a(n) = n iff n is prime. - Robert Israel, Mar 29 2015

Examples

			a(25) = gcd(5,25) = 5.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A099634, A099636.

Programs

Maple

seq(igcd(n, convert(numtheory:-factorset(n),`+`)), n = 1 .. 1000); # Robert Israel, Mar 29 2015

Mathematica

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