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%I #15 Sep 18 2023 19:41:59
%S 0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,
%T 0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,
%U 0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1
%N a(n) = 1 if n = 2 * p^k, with p an odd prime and k >= 1, otherwise 0.
%H Antti Karttunen, <a href="/A354981/b354981.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = [n == 2 (mod 4)] * A069513(n/2), where [ ] is the Iverson bracket.
%F For n > 4, a(n) = A211487(n) - A174275(n).
%t a[n_] := If[IntegerExponent[n, 2] == 1 && PrimePowerQ[n/2], 1, 0]; Array[a, 100] ( * _Amiram Eldar_, Jun 15 2022 *)
%t Module[{nn=150,c},c=Union[Flatten[Table[2 p^k,{p,Prime[Range[2,35]]},{k,5}]]];Table[If[ MemberQ[ c,k],1,0],{k,nn}]] (* _Harvey P. Dale_, Sep 18 2023 *)
%o (PARI) A354981(n) = (2==(n%4) && isprimepower(n/2));
%Y Characteristic function of A278568 \ {2}.
%Y Cf. A069513, A174275, A211487, A354108.
%K nonn
%O 1
%A _Antti Karttunen_, Jun 15 2022