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

1,4

Links

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

Formula

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

Maple

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

Prog

(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

Crossrefs

Cf. A008475, A067240.

Sequence in context: A135545 A123317 A231557 * A285707 A164879 A200219

Adjacent sequences: A171450 A171451 A171452 * A171454 A171455 A171456

Keyword

easy,nonn

Author

R. J. Mathar, Dec 09 2009

Status

approved