A347386 Number of iterations of A347385 (Dedekind psi function applied to the odd part of n) needed to reach a power of 2.

0, 0, 1, 0, 2, 1, 1, 0, 2, 2, 2, 1, 2, 1, 2, 0, 3, 2, 3, 2, 1, 2, 2, 1, 3, 2, 3, 1, 3, 2, 1, 0, 2, 3, 2, 2, 4, 3, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 2, 3, 3, 2, 4, 3, 3, 1, 3, 3, 3, 2, 2, 1, 2, 0, 2, 2, 4, 3, 2, 2, 3, 2, 5, 4, 3, 3, 2, 2, 3, 2, 4, 2, 2, 1, 4, 3, 3, 2, 4, 3, 2, 2, 1, 2, 3, 1, 3, 2, 3, 3, 4, 3, 3, 2, 2

Offset

1,5

Comments

Also, for n > 1, one less than the number of iterations of A347385 to reach 1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

If A209229(n) = 1, then a(n) = 0, otherwise a(n) = 1 + a(A001615(A000265(n))).

For all n >= 1, a(n) <= A331410(n).

Mathematica

f[p_, e_] := If[p == 2, 1, (p + 1)*p^(e - 1)]; psiOdd[1] = 1; psiOdd[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := -1 + Length @ NestWhileList[psiOdd, n, # != 2^IntegerExponent[#, 2] &]; Array[a, 100] (* Amiram Eldar, Aug 31 2021 *)

Prog

(PARI)
A347385(n) = if(1==n, n, my(f=factor(n>>valuation(n, 2))); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
A347386(n) = if(!bitand(n, n-1), 0, 1+A347386(A347385(n)));

Crossrefs

Cf. A000265, A001615, A209229, A347385, A347387 (the exponent of the eventual power of 2 reached).

Cf. also A003434, A019269, A227944, A256757, A331410, A336361 for similar sequences.

Sequence in context: A113974 A123331 A235141 * A331410 A336928 A366388

Adjacent sequences: A347383 A347384 A347385 * A347387 A347388 A347389

Keyword

nonn

Author

Antti Karttunen, Aug 31 2021

Status

approved