cp's OEIS Frontend

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.

%I A340676 #19 Feb 13 2021 14:39:48
%S A340676 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,
%T A340676 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,
%U A340676 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
%N 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.
%H A340676 Antti Karttunen, <a href="/A340676/b340676.txt">Table of n, a(n) for n = 1..65537</a>
%H A340676 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A340676 a(n) = A297109(A225546(n)).
%F A340676 For n > 1, a(n) = A104117(A267116(n)). - _Peter Munn_, Feb 05 2021
%t A340676 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 *)
%o A340676 (PARI)
%o A340676 A001511(n) = 1+valuation(n,2);
%o A340676 A209229(n) = (n && !bitand(n,n-1));
%o A340676 A104117(n) = (A209229(n)*A001511(n));
%o A340676 A267116(n) = if(n>1, fold(bitor, factor(n)[, 2]), 0);
%o A340676 A340676(n) = if(1==n,0,A104117(A267116(n)));
%Y A340676 Cf. A005117, A104117, A225546, A267116, A297109, A340673, A340675.
%Y A340676 Positions of zeros: {1} U A340681, of 1's: A005117 \ {1}, of 2's: A062503 \ {1}, of 3's: A113849.
%Y A340676 Positions of nonzero terms: A340682, of terms > 1: A340674.
%K A340676 nonn
%O A340676 1,4
%A A340676 _Antti Karttunen_, Feb 01 2021