A359784 - OEIS

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 #7 Jan 14 2023 12:40:03

%S 16,81,128,192,225,240,320,324,336,384,441,448,528,560,624,625,640,

%T 648,704,729,816,832,880,896,900,912,972,1024,1040,1088,1089,1104,

%U 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 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 (PARI)

%o A358680(n) = if(n<=1, 1, my(f=factor(n)); 0==((n*sum(i=1, #f~, f[i, 2]/f[i, 1]))%2));

%o memoA359780 = Map();

%o 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 A359781(n) = (A359780(n)%2);

%o isA359784(n) = (A358680(n)&&!(A359781(n)));

%Y Cf. A003415, A358680, A359780, A359781.

%Y Setwise difference A235992\{0} \ A359783.

%Y Setwise difference A359782 \ A235991.

%Y Subsequence of A013929.

%Y Cf. also A359767.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jan 13 2023