A136566 a(n) = sum of the exponents occurring only once each in the prime-factorization of n.

0, 1, 1, 2, 1, 0, 1, 3, 2, 0, 1, 3, 1, 0, 0, 4, 1, 3, 1, 3, 0, 0, 1, 4, 2, 0, 3, 3, 1, 0, 1, 5, 0, 0, 0, 0, 1, 0, 0, 4, 1, 0, 1, 3, 3, 0, 1, 5, 2, 3, 0, 3, 1, 4, 0, 4, 0, 0, 1, 2, 1, 0, 3, 6, 0, 0, 1, 3, 0, 0, 1, 5, 1, 0, 3, 3, 0, 0, 1, 5, 4, 0, 1, 2, 0, 0, 0, 4, 1, 2, 0, 3, 0, 0, 0, 6, 1, 3, 3, 0, 1, 0, 1, 4, 0

Offset: 1

Author

Leroy Quet, Jan 07 2008

Keywords

• nonn

Examples

			4200 = 2^3 * 3^1 * 5^2 * 7^1. The exponents of the prime factorization are therefore 3,1,2,1. The exponents occurring exactly once are 2 and 3. So a(4200) = 2+3 = 5.
		

Links

• Diana Mecum and Michael De Vlieger, Table of n, a(n) for n = 1..10000 (first 1000 terms from Diana Mecum)

Crossrefs

Cf. A136565, A136567.

Programs

Mathematica

Table[Total@ Flatten@ Select[Split[Sort[FactorInteger[n][[All, -1]]]], Length@ # == 1 &] - Boole[n == 1], {n, 105}] (* Michael De Vlieger, Sep 21 2017 *)

PARI

a(n) = my(f=factor(n)[,2]); sum(k=1, #f, f[k]*(#select(x->(x==f[k]), f) == 1)); \\ Michel Marcus, Sep 22 2017

Extensions

More terms from Diana L. Mecum, Jul 17 2008