A302777 - OEIS

%I #11 Nov 27 2020 04:51:24

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

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

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

%N a(n) = 1 if n is of the form p^(2^k) where p is prime and k >= 0, otherwise 0.

%C Characteristic function of "Fermi-Dirac primes", A050376.

%H Antti Karttunen, <a href="/A302777/b302777.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = A209229(A100995(n)).

%t a[n_] := Boole[n > 1 && Length[(f = FactorInteger[n])] == 1 && (e = f[[;; , 2]]) == 2^IntegerExponent[e, 2]]; Array[a, 100] (* _Amiram Eldar_, Nov 27 2020 *)

%o (PARI)

%o A209229(n) = (n && !bitand(n,n-1));

%o A302777(n) = A209229(isprimepower(n));

%o for(n=1,121,print1(A302777(n),","));

%Y Cf. A010051, A069513, A050376, A100995, A209229, A302778 (partial sums).

%K nonn

%O 1

%A _Antti Karttunen_, Apr 16 2018