A370131 a(n) = A068346(A276086(n)), where A068346 is the second arithmetic derivative, and A276086 is the primorial base exp-function.

0, 0, 0, 1, 5, 10, 0, 1, 12, 1, 16, 44, 7, 39, 16, 42, 608, 391, 55, 135, 365, 455, 1120, 2990, 800, 1100, 1400, 5425, 12575, 21025, 0, 6, 7, 1, 20, 103, 16, 1, 1, 32, 271, 320, 24, 78, 572, 459, 1031, 2887, 635, 1670, 1155, 3335, 19540, 22130, 4225, 7700, 18675, 28100, 68900, 155425, 9, 18, 20, 54, 704, 631, 24, 251

Offset: 0

Author

Antti Karttunen, Feb 10 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2559
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A068346, A276086, A327860, A370130.

Cf. A002110 (positions of 0's after the initial zero), A328233 (positions of 1's), A328240 (positions of primes), A369651 (= a(A143293(n-1)), for n >= 1).

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A370131(n) = A003415(A327860(n));

Formula

a(n) = A068346(A276086(n)) = A003415(A327860(n)).