A373144 Numbers k such that both A003415(k) and A276085(k) are multiples of 3, where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

1, 8, 27, 35, 36, 64, 65, 77, 95, 119, 125, 135, 143, 155, 161, 162, 180, 185, 189, 203, 209, 215, 216, 221, 252, 275, 280, 287, 288, 297, 299, 305, 323, 329, 335, 341, 343, 351, 365, 371, 377, 395, 396, 407, 413, 425, 437, 459, 468, 473, 485, 497, 512, 513, 515, 520, 527, 533, 545, 551, 575, 581, 605, 611, 612, 616

Offset

1,2

Comments

This is a multiplicative semigroup; if m and n are in the sequence then so is m*n.

Links

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

Example

65 is present as A003415(65) = 18 = 3*6 and A276085(65) = 2316 = 3*772.
77 is present as A003415(77) = 18 = 3*6 and A276085(77) = 240 = 3*80.
5005 (= 65*77) is present as A003415(5005) = A276085(5005) = 2556 = 3*852. (See A369650).

Prog

(PARI) \\ See A373143.

Crossrefs

Cf. A003415, A276085, A373143 (characteristic function).

Intersection of A327863 and A339746.

Positions of multiples of 3 in A373145.

Cf. also A369650.

Sequence in context: A355038 A297868 A051760 * A373373 A213519 A352423

Adjacent sequences: A373141 A373142 A373143 * A373145 A373146 A373147

Keyword

nonn

Author

Antti Karttunen, May 26 2024

Status

approved