A112621 If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = sum_{p|n} b(p,n)^b(p,n).

0, 1, 1, 4, 1, 2, 1, 27, 4, 2, 1, 5, 1, 2, 2, 256, 1, 5, 1, 5, 2, 2, 1, 28, 4, 2, 27, 5, 1, 3, 1, 3125, 2, 2, 2, 8, 1, 2, 2, 28, 1, 3, 1, 5, 5, 2, 1, 257, 4, 5, 2, 5, 1, 28, 2, 28, 2, 2, 1, 6, 1, 2, 5, 46656, 2, 3, 1, 5, 2, 3, 1, 31, 1, 2, 5, 5, 2, 3, 1, 257, 256, 2, 1, 6, 2, 2, 2, 28, 1, 6, 2, 5, 2, 2, 2, 3126, 1, 5, 5, 8, 1, 3, 1, 28, 3

Offset: 1

Author

Leroy Quet, Dec 25 2005

Keywords

• nonn

Comments

a(1) = 0 (empty sum). - Antti Karttunen, May 28 2017

Examples

			45 = 3^2 * 5^1. So a(45) = 2^2 + 1^1 = 5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A112622, A112623.

Programs

Mathematica

f[n_] := Block[{fi = Last@Transpose@FactorInteger@n}, Plus @@ (fi^fi)]; Rest@Array[f, 92] (* Robert G. Wilson v *)

PARI

A112621(n) = { my(f = factor(n), s = 0); for (k=1, #f~, s += (f[k, 2]^f[k, 2]); ); s; } \\ Antti Karttunen, May 28 2017

Formula

a(n) = 1 iff n is prime, a(n) = 2 iff n is a nonsquare semiprime (A006881). - Robert G. Wilson v, Dec 27 2005

Extensions

More terms from Robert G. Wilson v, Dec 27 2005

Term a(1) = 0 prepended, data section extended to 105 terms - Antti Karttunen, May 28 2017