A286583 a(n) = A007814(A048673(n)).

0, 1, 0, 0, 2, 3, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 5, 2, 2, 0, 2, 0, 1, 0, 1, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 3, 2, 0, 0, 0, 1, 4, 0, 1, 2, 1, 0, 1, 0, 0, 1, 1, 3, 1, 0, 2, 1, 2, 1, 0, 2, 0, 1, 3, 1, 0, 3, 3, 7, 1, 2, 0, 0, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 0, 4, 0, 5, 0, 1, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 6

Offset: 1

Author

Antti Karttunen, May 31 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007814, A048673, A286582, A286584, A286585.

Cf. A246261 (positions of zeros), A246263 (of nonzeros).

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus
A048673(n) = (A003961(n)+1)/2;
A007814(n) = (valuation(n,2));
A286583(n) = A007814(A048673(n));

Python

from sympy import factorint, nextprime, prod
def a007814(n): return 1 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")
def a048673(n):
    f = factorint(n)
    return 1 if n==1 else (1 + prod(nextprime(i)**f[i] for i in f))//2
def a(n): return a007814(a048673(n)) # Indranil Ghosh, Jun 12 2017

Scheme

(define (A286583 n) (A007814 (A048673 n)))

Formula

a(n) = A007814(A048673(n)).