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

Author

Antti Karttunen, Feb 11 2024

Keywords

• nonn

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.

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.

Programs

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)));