A336361 - OEIS

%I #17 Aug 30 2021 09:38:07

%S 0,0,1,0,2,1,1,0,3,2,2,1,2,1,2,0,4,3,3,2,1,2,2,1,2,2,3,1,3,2,1,0,2,4,

%T 2,3,4,3,2,2,2,1,3,2,3,2,2,1,4,2,4,2,4,3,4,1,3,3,3,2,2,1,3,0,2,2,5,4,

%U 2,2,4,3,5,4,2,3,2,2,3,2,5,2,2,1,4,3,3,2,4,3,2,2,1,2,3,1,5,4,3,2,5,4,3,2,2

%N Number of iterations of A000593 (sum of divisors of odd part of n) needed to reach a power of 2, or -1 if never reached.

%C Also, for n > 1, one less than the number of iterations of A000593 to reach 1.

%C If there exists any hypothetical odd perfect numbers w, then the iteration will get stuck into a fixed point after encountering them, and we will have a(w) = a(2^k * w) = -1 by the escape clause.

%H Antti Karttunen, <a href="/A336361/b336361.txt">Table of n, a(n) for n = 1..65537</a>

%F If A209229(n) = 1 [when n is a power of 2], a(n) = 0, otherwise a(n) = 1+a(A000593(n)).

%F a(n) = a(2n) = a(A000265(n)).

%o (PARI) A336361(n) = if(!bitand(n,n-1),0,1+A336361(sigma(n>>valuation(n,2))));

%Y Cf. A000265, A000593, A161942, A209229, A336362, A336363, A347249, A347250.

%Y Cf. A054784 (positions of 0's and 1's in this sequence).

%Y Cf. also A347240, A347241, A347242, A347243, A347244, A347245.

%K nonn

%O 1,5

%A _Antti Karttunen_, Jul 30 2020