A393049 Composite numbers k such that k is a multiple of A276085(A003415(k)), where A003415 is the arithmetic derivative and A276085 is fully additive with a(p) = p#/p.

4, 6, 8, 9, 12, 15, 20, 21, 50, 64, 65, 95, 108, 135, 144, 160, 180, 189, 320, 329, 432, 481, 623, 869, 1024, 1072, 1199, 1280, 1458, 1639, 2257, 2700, 2912, 3341, 3408, 3456, 3564, 3933, 4032, 4511, 4802, 5292, 6071, 6750, 7168, 7290, 7361, 7500, 7776, 9383, 11500, 11664, 12798, 13201, 13248, 14580, 15660, 17136

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..1492

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); };
is_A393049(n) = (n>1 && !isprime(n) && !(n%A276085(A003415(n))));

Crossrefs

Cf. A003415, A276085, A393050 (subsequence).

Subsequence of A393048.

Cf. also A373490.

Sequence in context: A157942 A122786 A092630 * A079142 A062002 A090419

Adjacent sequences: A393046 A393047 A393048 * A393050 A393051 A393052

Keyword

nonn

Author

Antti Karttunen, Feb 06 2026

Status

approved