A336361 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.

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, 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, 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

Offset

1,5

Comments

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

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.

Links

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

Formula

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

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

Prog

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

Crossrefs

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

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

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

Sequence in context: A277721 A023416 A080791 * A364260 A334204 A336362

Adjacent sequences: A336358 A336359 A336360 * A336362 A336363 A336364

Keyword

nonn

Author

Antti Karttunen, Jul 30 2020

Status

approved