A373849 Difference between the primorial base exp-function and the arithmetic derivative.

1, 2, 2, 5, 5, 17, 0, 9, 3, 24, 38, 89, 9, 49, 66, 142, 193, 449, 104, 249, 351, 740, 1112, 2249, 581, 1240, 1860, 3723, 5593, 11249, -24, 13, -59, 28, 44, 114, -25, 69, 84, 194, 247, 629, 134, 349, 477, 1011, 1550, 3149, 763, 1736, 2580, 5230, 7819, 15749, 4294, 8734, 13033, 26228, 39344, 78749, -43, 97, 114, 243

Offset: 0

Author

Antti Karttunen, Jun 23 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 0..30030
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A327858 [= gcd(a(n), A003415(n))], A351228 (indices of nonpositive terms).

Cf. A328382, A369971, A373603.

Cf. A359821 (positions of even terms), A359822 (of odd terms).

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); };
A373849(n) = (A276086(n)-A003415(n));

Formula

a(n) = A276086(n) - A003415(n).