A318316 Multiplicative with a(p^e) = 2^A007306(e).

1, 2, 2, 4, 2, 4, 2, 8, 4, 4, 2, 8, 2, 4, 4, 8, 2, 8, 2, 8, 4, 4, 2, 16, 4, 4, 8, 8, 2, 8, 2, 16, 4, 4, 4, 16, 2, 4, 4, 16, 2, 8, 2, 8, 8, 4, 2, 16, 4, 8, 4, 8, 2, 16, 4, 16, 4, 4, 2, 16, 2, 4, 8, 32, 4, 8, 2, 8, 4, 8, 2, 32, 2, 4, 8, 8, 4, 8, 2, 16, 8, 4, 2, 16, 4, 4, 4, 16, 2, 16, 4, 8, 4, 4, 4, 32, 2, 8, 8, 16, 2, 8, 2, 16, 8

Offset: 1

Author

Antti Karttunen, Aug 31 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. A007306, A318307, A318322.

Programs

PARI

A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
A007306(n) = if(!n,1,A002487(n+n-1));
A318316(n) = factorback(apply(e -> 2^A007306(e),factor(n)[,2]));

Python

from functools import reduce
from sympy import factorint
def A318316(n): return 1<Chai Wah Wu, May 18 2023

Formula

a(n) = 2^A318322(n).

a(n) = A318307(A003557(n^2)) = A318307(A003557(n))*A318307(n).