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A318316
Multiplicative with a(p^e) = 2^A007306(e).
3
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
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
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Aug 31 2018
STATUS
approved