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

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.

If it exists, a(13) > 1241513984.

Links

Table of n, a(n) for n=1..12.

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)));

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.

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

Cf. also A369970, A370114.

Sequence in context: A181474 A047187 A048043 * A043429 A105041 A138632

Adjacent sequences: A370112 A370113 A370114 * A370116 A370117 A370118

Keyword

nonn

Author

Antti Karttunen, Feb 11 2024

Status

approved