A392593 Numbers k such that A003415(k) == A276085(k) (mod 3), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

1, 2, 8, 10, 12, 15, 22, 24, 27, 28, 32, 33, 34, 35, 36, 46, 51, 52, 58, 64, 65, 69, 76, 77, 82, 84, 87, 94, 95, 100, 105, 106, 118, 119, 123, 124, 125, 128, 135, 140, 141, 142, 143, 148, 155, 156, 159, 161, 162, 166, 168, 172, 177, 178, 180, 185, 189, 195, 202, 203, 209, 213, 214, 215, 216, 220, 221, 226, 228, 231

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

{k such that A373253(k) == A373153(k)}.

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_A392593(n) = !((A276085(n)-A003415(n))%3);
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
is_A392593(n) = !((A003415(n)-(valuation(n, 2)-valuation(n, 3)))%3);

Crossrefs

Cf. A003415, A276085, A373253, A373153.

Subsequences: A369650, A373144, A391864.

Sequence in context: A081693 A022298 A229090 * A265670 A297999 A287088

Adjacent sequences: A392590 A392591 A392592 * A392594 A392595 A392596

Keyword

nonn

Author

Antti Karttunen, Jan 17 2026

Status

approved