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
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..65537
Programs
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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 *) -
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));
Comments