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A359784 Numbers k such that A358680(k) = 1 but A359781(k) = 0, where A359781 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with even arithmetic derivative).

%I A359784 #7 Jan 14 2023 12:40:03
%S A359784 16,81,128,192,225,240,320,324,336,384,441,448,528,560,624,625,640,
%T A359784 648,704,729,816,832,880,896,900,912,972,1024,1040,1088,1089,1104,
%U A359784 1215,1216,1225,1232,1360,1392,1408,1456,1472,1488,1520,1521,1620,1664,1701,1764,1776,1800,1840,1856,1904,1920,1944,1968,1984
%N A359784 Numbers k such that A358680(k) = 1 but A359781(k) = 0, where A359781 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with even arithmetic derivative).
%o A359784 (PARI)
%o A359784 A358680(n) = if(n<=1, 1, my(f=factor(n)); 0==((n*sum(i=1, #f~, f[i, 2]/f[i, 1]))%2));
%o A359784 memoA359780 = Map();
%o A359784 A359780(n) = if(1==n,1,my(v); if(mapisdefined(memoA359780,n,&v), v, v = -sumdiv(n,d,if(d<n,A358680(n/d)*A359780(d),0)); mapput(memoA359780,n,v); (v)));
%o A359784 A359781(n) = (A359780(n)%2);
%o A359784 isA359784(n) = (A358680(n)&&!(A359781(n)));
%Y A359784 Cf. A003415, A358680, A359780, A359781.
%Y A359784 Setwise difference A235992\{0} \ A359783.
%Y A359784 Setwise difference A359782 \ A235991.
%Y A359784 Subsequence of A013929.
%Y A359784 Cf. also A359767.
%K A359784 nonn
%O A359784 1,1
%A A359784 _Antti Karttunen_, Jan 13 2023