A336916 One more than the number of iterations of x -> 2x needed before the result is nondeficient, when starting from x=n; a(n) = 0, when n is a power of 2.

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

Offset

1,3

Comments

See comments in A336915.

Links

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

Mathematica

a[n_] := Module[{e = IntegerExponent[n, 2], s}, If[n == 2^e, 0, s = DivisorSigma[-1, n/2^e]; Max[Ceiling[Log2[s/(s - 1)]] - e, 1]]]; Array[a, 100] (* Amiram Eldar, Apr 01 2024 *)

Prog

(PARI) A336916(n) = if(!bitand(n, n-1), 0, for(i=1, oo, my(n2 = n+n); if(sigma(n) >= n2, return(i)); n = n2));

Crossrefs

One more than A336915.

Cf. also A279048, A336835.

Sequence in context: A167565 A199470 A098006 * A082650 A054875 A324115

Adjacent sequences: A336913 A336914 A336915 * A336917 A336918 A336919

Keyword

nonn

Author

Antti Karttunen, Aug 08 2020

Status

approved