A171453 a(n) = sum_i p_i^(e_i-1) where n = product_i p_i^e_i is the prime number decomposition of n.

0, 1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 3, 1, 2, 2, 8, 1, 4, 1, 3, 2, 2, 1, 5, 5, 2, 9, 3, 1, 3, 1, 16, 2, 2, 2, 5, 1, 2, 2, 5, 1, 3, 1, 3, 4, 2, 1, 9, 7, 6, 2, 3, 1, 10, 2, 5, 2, 2, 1, 4, 1, 2, 4, 32, 2, 3, 1, 3, 2, 3, 1, 7, 1, 2, 6, 3, 2, 3, 1, 9, 27, 2, 1, 4, 2, 2, 2, 5, 1, 5, 2, 3, 2, 2, 2, 17, 1, 8, 4, 7

Offset: 1

Author

R. J. Mathar, Dec 09 2009

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A008475, A067240.

Programs

Maple

A171453 := proc(n) add( op(1,f)^(op(2,f)-1),f =ifactors(n)[2]) ; end proc:
seq(A171453(n),n=1..100) ;

PARI

A171453(n) = { my(f=factor(n)); vecsum(vector(#f~,i,f[i,1]^(f[i,2]-1))); }; \\ Antti Karttunen, Sep 24 2017

Python

from sympy import factorint
def A171453(n): return sum(p**(e-1) for p,e in factorint(n).items()) # Chai Wah Wu, Jul 01 2024

Formula

a(n) = A008475(n) - A067240(n).