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A340676
If n is of the form s^(2^e), where s is a squarefree number, and e >= 0, then a(n) = 1+e, otherwise a(n) = 0.
4
0, 1, 1, 2, 1, 1, 1, 0, 2, 1, 1, 0, 1, 1, 1, 3, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 3, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 2, 1, 1, 1, 0, 1
OFFSET
1,4
FORMULA
a(n) = A297109(A225546(n)).
For n > 1, a(n) = A104117(A267116(n)). - Peter Munn, Feb 05 2021
MATHEMATICA
a[1] = 0; a[n_] := If[Length[(u = Union[FactorInteger[n][[;; , 2]]])] == 1 && u[[1]] == 2^(e = IntegerExponent[u[[1]], 2]), e + 1, 0]; Array[a, 100] (* Amiram Eldar, Feb 10 2021 *)
PROG
(PARI)
A001511(n) = 1+valuation(n, 2);
A209229(n) = (n && !bitand(n, n-1));
A104117(n) = (A209229(n)*A001511(n));
A267116(n) = if(n>1, fold(bitor, factor(n)[, 2]), 0);
A340676(n) = if(1==n, 0, A104117(A267116(n)));
CROSSREFS
Positions of zeros: {1} U A340681, of 1's: A005117 \ {1}, of 2's: A062503 \ {1}, of 3's: A113849.
Positions of nonzero terms: A340682, of terms > 1: A340674.
Sequence in context: A286935 A090340 A287364 * A117162 A277045 A146061
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 01 2021
STATUS
approved