A318474 Multiplicative with a(p^e) = 2^A000045(e+1).

1, 2, 2, 4, 2, 4, 2, 8, 4, 4, 2, 8, 2, 4, 4, 32, 2, 8, 2, 8, 4, 4, 2, 16, 4, 4, 8, 8, 2, 8, 2, 256, 4, 4, 4, 16, 2, 4, 4, 16, 2, 8, 2, 8, 8, 4, 2, 64, 4, 8, 4, 8, 2, 16, 4, 16, 4, 4, 2, 16, 2, 4, 8, 8192, 4, 8, 2, 8, 4, 8, 2, 32, 2, 4, 8, 8, 4, 8, 2, 64, 32, 4, 2, 16, 4, 4, 4, 16, 2, 16, 4, 8, 4, 4, 4, 512, 2, 8, 8, 16, 2, 8, 2, 16, 8

Offset: 1

Author

Antti Karttunen, Aug 29 2018

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A000045, A318465, A318472, A318473.

Programs

Mathematica

Array[Apply[Times, 2^Fibonacci[# + 1] & /@ FactorInteger[#][[All, -1]]] - Boole[# == 1] &, 105] (* Michael De Vlieger, Sep 02 2018 *)

PARI

A318474(n) = factorback(apply(e -> 2^fibonacci(1+e),factor(n)[,2]));

Formula

a(n) = 2^A318473(n).

a(n) = A318472(A064549(n)).

a(A064549(n)) = a(n)*A318472(n).