OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = A153151(p^e). - Antti Karttunen, Jul 01 2021
Sum_{k=1..n} a(k) ~ c * n^2, where c = (4/5) * Product_{p prime} (1 - 1/(p*(p+1))) = (4/5) * A065463 = 0.563553... . - Amiram Eldar, Nov 18 2022
MATHEMATICA
f[2, e_] := 2^(e + 1) - 1; f[p_, e_] := p^e - 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jun 03 2021 *)
PROG
(PARI) A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
(Python 3.8+)
from math import prod
from sympy import factorint
def A344875(n): return prod((p**(1+e) if p == 2 else p**e)-1 for p, e in factorint(n).items()) # Chai Wah Wu, Jun 01 2022
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Jun 03 2021
STATUS
approved