A358765 a(n) = A003415(n)*A276086(n) mod 60, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

0, 0, 3, 6, 36, 18, 25, 10, 0, 0, 15, 30, 40, 50, 15, 0, 0, 30, 45, 10, 0, 0, 45, 30, 20, 20, 45, 30, 0, 30, 37, 14, 0, 48, 57, 12, 0, 10, 45, 0, 0, 30, 35, 50, 0, 30, 15, 30, 20, 20, 45, 0, 0, 30, 15, 20, 0, 0, 45, 30, 8, 38, 51, 54, 12, 36, 5, 10, 0, 0, 15, 30, 0, 50, 45, 30, 0, 0, 55, 10, 0, 0, 15

Offset: 0

Author

Antti Karttunen, Dec 06 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..60060
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A358669, A358850.

Cf. A016825 (positions of odd terms), A042965 (of even terms), A235992 (of multiples of 4), A067019 (of terms of the form 4k+2).

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); };
A358765(n) = ((A003415(n)*A276086(n))%60);

Formula

a(n) = A358669(n) mod 60.