%I #12 May 15 2022 17:21:07
%S 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,
%U 0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0
%N a(n) = 1 if n is either 4th power of a prime (A030514), or product of a prime and the square of a different prime (A054753), otherwise 0.
%H Antti Karttunen, <a href="/A353798/b353798.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F a(n) = [floor(A101296(n)/2) == 3], where [ ] is the Iverson bracket, giving in this case 1 only if the prime signature class of n (A101296) is either 6 or 7.
%F a(n) >= A353472(n).
%t a[n_] := If[MemberQ[{{4}, {1, 2}, {2, 1}}, FactorInteger[n][[;; , 2]]], 1, 0]; Array[a, 100] (* _Amiram Eldar_, May 13 2022 *)
%o (PARI) A353798(n) = { my(f=factor(n)[, 2]~); (f==[4] || f==[2, 1] || f==[1, 2]); }; \\ From function "is" in A080258
%Y Characteristic function of A080258.
%Y Cf. A030514, A054753, A101296, A353472.
%K nonn
%O 1
%A _Antti Karttunen_, May 13 2022