A286583 - OEIS

%I #14 May 25 2020 03:42:53

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A286583/b286583.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (PARI)

%o 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_

%o A048673(n) = (A003961(n)+1)/2;

%o A007814(n) = (valuation(n,2));

%o A286583(n) = A007814(A048673(n));

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

%o (Python)

%o from sympy import factorint, nextprime, prod

%o def a007814(n): return 1 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")

%o def a048673(n):

%o     f = factorint(n)

%o     return 1 if n==1 else (1 + prod(nextprime(i)**f[i] for i in f))//2

%o def a(n): return a007814(a048673(n)) # _Indranil Ghosh_, Jun 12 2017

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

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

%K nonn

%O 1,5

%A _Antti Karttunen_, May 31 2017