A344875 Multiplicative with a(2^e) = 2^(1+e) - 1, and a(p^e) = p^e - 1 for odd primes p.

1, 3, 2, 7, 4, 6, 6, 15, 8, 12, 10, 14, 12, 18, 8, 31, 16, 24, 18, 28, 12, 30, 22, 30, 24, 36, 26, 42, 28, 24, 30, 63, 20, 48, 24, 56, 36, 54, 24, 60, 40, 36, 42, 70, 32, 66, 46, 62, 48, 72, 32, 84, 52, 78, 40, 90, 36, 84, 58, 56, 60, 90, 48, 127, 48, 60, 66, 112, 44, 72, 70, 120, 72, 108, 48, 126, 60, 72, 78, 124, 80, 120

Offset

1,2

Links

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

Formula

a(n) = A344878(n) * A344879(n).

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

Cf. A047994, A065463, A153151, A344876, A344877, A344878, A344879, A344969, A345947.

Sequence in context: A360960 A371974 A344878 * A178910 A182651 A175055

Adjacent sequences: A344872 A344873 A344874 * A344876 A344877 A344878

Keyword

nonn,mult

Author

Antti Karttunen, Jun 03 2021

Status

approved