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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from exponents in factorization of n

Formula

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

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

Prog

(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<<sum(sum(reduce(lambda x, y:(x[0], sum(x)) if int(y) else (sum(x), x[1]), bin((e<<1)-1)[-1:2:-1], (1, 0))) for e in factorint(n).values()) # Chai Wah Wu, May 18 2023

Crossrefs

Cf. A007306, A318307, A318322.

Sequence in context: A085191 A188581 A347958 * A328721 A165872 A061142

Adjacent sequences: A318313 A318314 A318315 * A318317 A318318 A318319

Keyword

nonn,mult

Author

Antti Karttunen, Aug 31 2018

Status

approved