A370115 Numbers k for which k is a multiple of A276086(A003415(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

0, 1, 2, 10, 15, 161, 2189, 5005, 27030, 29861, 510221, 223092341, 1310518729

Offset

1,3

Comments

Question: Is the squarefreeness a necessary condition for the nonzero terms of this sequence?

Many of the terms occur also in A368703, because the arithmetic derivative of those terms is one of the primorial numbers, A002110.

Links

Table of n, a(n) for n=1..13.

Formula

{k such that k is a multiple of A327859(k)}. - Antti Karttunen, Jan 31 2026

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA370115(n) = !(n%A276086(A003415(n)));
(PARI) is_A370115(n) = if(n<3, 1, if(isprime(n), 0, my(f=factor(n), u = n*sum(i=1, #f~, f[i, 2]/f[i, 1]), m=1, p=2, pp); while(u, if((pp=(p^(u%p)))>1, m *= pp; if(n%pp, return(0))); u \= p; p = nextprime(1+p)); !(n%m))); \\ Antti Karttunen, Jan 27 2026

Crossrefs

Positions of 1's in A370117, positions of 0's in A370120.

Intersection of A048103 and A369650 is a subsequence of this sequence. See the comments in latter.

Subsequence of A392867, and probably also of A392868.

Cf. A002110, A003415, A276086, A327859, A368703, A380459, A392878.

Cf. also A369970, A370114.

Sequence in context: A392607 A047187 A048043 * A387658 A043429 A105041

Adjacent sequences: A370112 A370113 A370114 * A370116 A370117 A370118

Keyword

nonn

Author

Antti Karttunen, Feb 11 2024

Extensions

a(13) added by Antti Karttunen, Jan 30 2026

Status

approved