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

1,4

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A136565, A136567.

Sequence in context: A329615 A272894 A268387 * A330235 A048983 A301505

Adjacent sequences: A136563 A136564 A136565 * A136567 A136568 A136569

Keyword

nonn

Author

Leroy Quet, Jan 07 2008

Extensions

More terms from Diana L. Mecum, Jul 17 2008

Status

approved