A344879 a(n) = A344875(n) / A344878(n), where A344875(n) is multiplicative with a(2^e) = 2^(1+e) - 1, and a(p^e) = p^e -1 for odd primes p, and A344878(n) gives the least common multiple of the same factors.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 3, 2, 1, 1, 6, 1, 1, 4, 1, 1, 1, 1, 3, 2, 1, 1, 1, 2, 3, 2, 1, 1, 2, 1, 3, 2, 1, 4, 2, 1, 1, 2, 6, 1, 1, 1, 3, 2, 1, 2, 6, 1, 1, 1, 1, 1, 2, 4, 3, 2, 5, 1, 4, 6, 1, 2, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 3, 4

Offset

1,14

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Mathematica

f[2, e_] := 2^(e + 1) - 1; f[p_, e_] := p^e - 1; a[1] = 1; a[n_] := Times @@ (fct = f @@@ FactorInteger[n])/LCM @@ fct; 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)); };
A344878(n) = if(1==n, n, my(f=factor(n)~); lcm(vector(#f, i, (f[1, i]^(f[2, i]+(2==f[1, i]))-1))));
A344879(n) = (A344875(n) / A344878(n));
(Python)
from math import prod, lcm
from sympy import factorint
def A344879(n): return prod(a := tuple(p**(e+int(p==2))-1 for p, e in factorint(n).items()))//lcm(*a) # Chai Wah Wu, Jun 15 2022

Crossrefs

Cf. A344875, A344878.

Sequence in context: A357477 A172083 A337199 * A090189 A227141 A284997

Adjacent sequences: A344876 A344877 A344878 * A344880 A344881 A344882

Keyword

nonn

Author

Antti Karttunen, Jun 03 2021

Status

approved