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

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..30030

Index entries for sequences related to primorial base

Formula

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

Prog

(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));

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).

Sequence in context: A245849 A245850 A245844 * A083849 A326512 A325983

Adjacent sequences: A373846 A373847 A373848 * A373850 A373851 A373852

Keyword

sign

Author

Antti Karttunen, Jun 23 2024

Status

approved