A318322 Additive with a(p^e) = A007306(e).

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 4, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 4, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 3, 5, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 4, 3, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 3, 2, 2, 2, 5, 1, 3, 3, 4, 1, 3, 1, 4, 3

Offset

1,4

Links

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

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A007814(A318316(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));
A318322(n) = vecsum(apply(e -> A007306(e), factor(n)[, 2]));
(Python)
from functools import reduce
from sympy import factorint
def A318322(n): return 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, A318306, A318316.

Differs from A122810 for the first time at n=48, where a(48) = 4, while A122810(48) = 5.

Sequence in context: A125030 A116479 A366989 * A122810 A179953 A277013

Adjacent sequences: A318319 A318320 A318321 * A318323 A318324 A318325

Keyword

nonn

Author

Antti Karttunen, Aug 31 2018

Status

approved