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

1,1

Links

Table of n, a(n) for n=1..57.

Prog

(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(d<n, A358680(n/d)*A359780(d), 0)); mapput(memoA359780, n, v); (v)));
A359781(n) = (A359780(n)%2);
isA359784(n) = (A358680(n)&&!(A359781(n)));

Crossrefs

Cf. A003415, A358680, A359780, A359781.

Setwise difference A235992\{0} \ A359783.

Setwise difference A359782 \ A235991.

Subsequence of A013929.

Cf. also A359767.

Sequence in context: A339596 A088040 A354799 * A346484 A065771 A320965

Adjacent sequences: A359781 A359782 A359783 * A359785 A359786 A359787

Keyword

nonn

Author

Antti Karttunen, Jan 13 2023

Status

approved