A358669 Pointwise product of the arithmetic derivative and the primorial base exp-function.

0, 0, 3, 6, 36, 18, 25, 10, 180, 180, 315, 90, 400, 50, 675, 1200, 7200, 450, 2625, 250, 9000, 7500, 14625, 2250, 27500, 12500, 28125, 101250, 180000, 11250, 217, 14, 1680, 588, 1197, 1512, 2100, 70, 2205, 3360, 21420, 630, 7175, 350, 25200, 40950, 39375, 3150, 98000, 24500, 118125, 105000, 441000

Offset: 0

Author

Antti Karttunen, Dec 05 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..11550
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..60060
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A059841, A121262, A152822, A276086, A327858, A353558, A358680, A358765 (= a(n) mod 60), A359423, A359603 [Dirichlet inverse of 1+a(n)].

Cf. A016825 (positions of odd terms), A042965 (of even terms), A235992 (of multiples of 4), A067019 (of terms of the form 4k+2), A358748 (of the form 4k+1), A358749 (of the form 4k+3).

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); };
A358669(n) = (A003415(n)*A276086(n));

Formula

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

From Antti Karttunen, Jan 09 2023: (Start)

a(n) = A327858(n) * A359423(n).

For all n >= 0, A059841(a(n)) = A152822(n).

For all n >= 1, 1-A152822(a(n)) = A353558(n).

For all n >= 0, A121262(a(n)) = A358680(n).

(End)