A347387 The exponent of the first power of 2 reached when starting iterating A347385 from n, where A347385 is Dedekind psi function applied to the odd part of n.

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

Offset

1,3

Links

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

Formula

a(2^k) = k, and for numbers with A209229(n) = 0, a(n) = a(A001615(A000265(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_] := IntegerExponent[NestWhile[psiOdd, n, # != 2^IntegerExponent[#, 2] &], 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)));
A347387(n) = if(!bitand(n, n-1), valuation(n, 2), A347387(A347385(n)));

Crossrefs

Cf. A000265, A001615, A007814, A209229, A347385, A347386.

Cf. also A049113, A347388.

Sequence in context: A322665 A368857 A273632 * A196046 A152724 A081743

Adjacent sequences: A347384 A347385 A347386 * A347388 A347389 A347390

Keyword

nonn

Author

Antti Karttunen, Aug 31 2021

Status

approved