A373490 Numbers k for which A003415(k) is a multiple of A276085(k), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

1, 2, 4, 8, 10, 12, 15, 16, 20, 28, 32, 36, 64, 100, 108, 128, 144, 162, 180, 189, 192, 216, 225, 256, 400, 480, 500, 512, 686, 784, 972, 1000, 1024, 1250, 1280, 1296, 1350, 1728, 1890, 2048, 2160, 2304, 2700, 2835, 2880, 3375, 3500, 3600, 3840, 4032, 4096, 4500, 4800, 4860, 5005, 5096, 5120, 6300, 6400, 6480, 6750

Offset

1,2

Comments

Conjecture: if term present here is squarefree, then it must be a term of A369650: 1, 2, 10, 15, 5005, and possibly no others. Or put in other words, if A003415(k) = e*A276085(k), then if e > 1, it is conjectured that k cannot be squarefree (in A005117).

Links

Antti Karttunen, Table of n, a(n) for n = 1..1710

Formula

{k such that A276085(A380459(k)) = A276085(k^e) for some e >= 1}. - Antti Karttunen, Jan 29 2026

Prog

(PARI) isA373490 = A373489;

Crossrefs

Cf. A003415, A005117, A276085, A373489 (characteristic function), A380459.

Subsequence of A392869.

Subsequences: A000079, A369650.

After the initial 1, gives the positions of 0's in A373147.

Cf. also A373487, A373488.

Sequence in context: A001770 A032494 A125953 * A394895 A308357 A047464

Adjacent sequences: A373487 A373488 A373489 * A373491 A373492 A373493

Keyword

nonn

Author

Antti Karttunen, Jun 09 2024

Status

approved