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a(n) = 1 if n is a power of prime with an even exponent, otherwise 0.
2

%I #11 May 15 2022 23:49:10

%S 1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

%N a(n) = 1 if n is a power of prime with an even exponent, otherwise 0.

%H Antti Karttunen, <a href="/A353800/b353800.txt">Table of n, a(n) for n = 1..100489</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) = A010055(n) - A353817(n).

%F a(n) >= A302048(n).

%e a(1) = 1 because 1 = p^0 for any prime p, and 0 is an even number.

%t a[n_] := If[n == 1 || (Length[(f = FactorInteger[n])] == 1 && EvenQ[f[[1, 2]]]), 1, 0]; Array[a, 100] (* _Amiram Eldar_, May 15 2022 *)

%o (PARI) A353800(n) = ((1==n)||((n=isprimepower(n))&&!(n%2)));

%Y Characteristic function of A056798.

%Y Cf. A010055, A302048, A353817.

%K nonn

%O 1

%A _Antti Karttunen_, May 15 2022