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A286583 a(n) = A007814(A048673(n)). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

FORMULA

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

PROG

(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));

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

(Python)

from sympy import factorint, nextprime

from operator import mul

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 + reduce(mul, [nextprime(i)**f[i] for i in f]))/2

def a(n): return a007814(a048673(n)) # Indranil Ghosh, Jun 12 2017

CROSSREFS

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

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

Sequence in context: A171996 A175669 A288839 * A321931 A321934 A004579

Adjacent sequences:  A286580 A286581 A286582 * A286584 A286585 A286586

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 31 2017

STATUS

approved

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Last modified April 5 16:49 EDT 2020. Contains 333245 sequences. (Running on oeis4.)