A373487 Numbers k such that A276085(k) is a multiple of A003415(k), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

1, 2, 3, 5, 7, 10, 11, 13, 15, 17, 19, 23, 28, 29, 31, 35, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 143, 149, 151, 155, 157, 161, 163, 167, 173, 179, 181, 187, 191, 193, 197, 199, 203, 209, 211, 215, 221, 223, 227, 229, 233, 239, 241, 251, 257, 263

Offset

1,2

Comments

Sequence A276086(A380527(.)) when sorted into ascending order gives the {intersection of this sequence with A048103}. As A380527 is a subsequence of A381035, this intersection is by the given correspondence a subsequence of (primes U A080364). Note that this applies also to the third known nonsquarefree term of this sequence, 855523 (= 67 * 113^2), which indeed disproves the conjecture I had made in A380527, while the first two nonsquarefree terms 28 and 33212 are both multiples of 4, and thus outside of the intersection.- Antti Karttunen, Jan 28 2026

Links

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

Prog

(PARI) isA373487 = A373486;

Crossrefs

Cf. A003415, A080364, A276085, A276086, A369650 (subsequence), A373486 (characteristic function), A380527.

After the initial 1, gives the positions of 0's in A373148.

Disjoint union of A000040 and A373488 (nonprime terms).

Cf. also A373489, A391845.

Sequence in context: A002269 A327445 A325119 * A047487 A327203 A048461

Adjacent sequences: A373484 A373485 A373486 * A373488 A373489 A373490

Keyword

nonn

Author

Antti Karttunen, Jun 09 2024

Status

approved