A383299 Numbers k such that A276086(k) is a multiple of A276086(A003415(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

0, 1, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 23, 27, 29, 31, 37, 41, 43, 45, 47, 51, 53, 59, 61, 67, 71, 73, 79, 83, 87, 89, 97, 101, 103, 107, 109, 113, 117, 119, 127, 131, 137, 139, 141, 147, 149, 151, 157, 161, 163, 165, 167, 171, 173, 177, 179, 181, 191, 193, 197, 199, 203, 207, 209, 211, 223, 227, 229, 233, 239

Offset

1,3

Comments

The sequence contains the intersection of A048103, A369650, and A328387. That is, {1, 15, 5005}, at least.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to primorial base.

Example

5 is a term as A003415(5) = 1, and A276086(5) = 18 is a multiple of A276086(1) = 2, and ditto for all odd primes.
9 is a term as A003415(9) = 6, and A276086(9) = 30 is a multiple of A276086(6) = 5.
15 is a term as A003415(15) = 8, and A276086(15) = 150 is a multiple of A276086(8) = 15.
5005 is a term as A003415(5005) = 2556, and A276086(5005) = 39055266250 = 7803250 * A276086(2556) = 7803250 * 5005. See also A369650.
See also examples in A383300.

Prog

(PARI) isA383299 = A383298;

Crossrefs

Cf. A003415, A048103, A276086, A327859, A328387, A383298 (characteristic function).

Cf. A006005, A051674, A383300, A383301 (subsequences).

Cf. also A369650.

Sequence in context: A161153 A128201 A347301 * A233514 A096262 A308168

Adjacent sequences: A383296 A383297 A383298 * A383300 A383301 A383302

Keyword

nonn

Author

Antti Karttunen, May 15 2025

Status

approved