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).

16, 81, 128, 192, 225, 240, 320, 324, 336, 384, 441, 448, 528, 560, 624, 625, 640, 648, 704, 729, 816, 832, 880, 896, 900, 912, 972, 1024, 1040, 1088, 1089, 1104, 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

Offset: 1

Author

Antti Karttunen, Jan 13 2023

Keywords

• nonn

Crossrefs

Cf. A003415, A358680, A359780, A359781.

Setwise difference A235992\{0} \ A359783.

Setwise difference A359782 \ A235991.

Subsequence of A013929.

Cf. also A359767.

Programs

PARI

A358680(n) = if(n<=1, 1, my(f=factor(n)); 0==((n*sum(i=1, #f~, f[i, 2]/f[i, 1]))%2));
memoA359780 = Map();
A359780(n) = if(1==n,1,my(v); if(mapisdefined(memoA359780,n,&v), v, v = -sumdiv(n,d,if(dA358680(n/d)*A359780(d),0)); mapput(memoA359780,n,v); (v)));
A359781(n) = (A359780(n)%2);
isA359784(n) = (A358680(n)&&!(A359781(n)));