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%I #15 Nov 27 2020 04:51:42
%S 0,1,2,3,4,4,5,5,6,6,7,7,8,8,8,9,10,10,11,11,11,11,12,12,13,13,13,13,
%T 14,14,15,15,15,15,15,15,16,16,16,16,17,17,18,18,18,18,19,19,20,20,20,
%U 20,21,21,21,21,21,21,22,22,23,23,23,23,23,23,24,24,24,24,25,25,26,26,26,26,26,26,27,27,28,28,29,29,29,29,29,29,30
%N Number of "Fermi-Dirac primes" (A050376) <= n.
%H Antti Karttunen, <a href="/A302778/b302778.txt">Table of n, a(n) for n = 1..65537</a>
%F a(1) = 0; for n > 1, a(n) = A302777(n) + a(n-1).
%F For all n >= 1, a(A050376(n)) = n.
%t s[n_] := Boole[n > 1 && Length[(f = FactorInteger[n])] == 1 && (e = f[[;; , 2]]) == 2^IntegerExponent[e, 2]]; Accumulate @ Array[s, 100] (* _Amiram Eldar_, Nov 27 2020 *)
%o (PARI)
%o A209229(n) = (n && !bitand(n,n-1));
%o A302777(n) = A209229(isprimepower(n));
%o s=0; for(n=1,105,s+=A302777(n); print1(s,", "));
%Y Partial sums of A302777. A left inverse of A050376.
%Y Cf. A302785, A302786.
%Y Differs from A203967 for the first time at n=64, where a(64) = 23, while A203967(64) = 24.
%Y Cf. also A000720, A025528.
%K nonn
%O 1,3
%A _Antti Karttunen_, Apr 16 2018
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