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.

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

Author

Antti Karttunen, Feb 01 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A005117, A104117, A225546, A267116, A297109, A340673, A340675.

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.

Programs

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 *)

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)));

Formula

a(n) = A297109(A225546(n)).

For n > 1, a(n) = A104117(A267116(n)). - Peter Munn, Feb 05 2021