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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.
4
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 31 2021
STATUS
approved