A373158 Fully additive with a(p) = p# for prime p, where x# is the primorial A034386(x).

0, 2, 6, 4, 30, 8, 210, 6, 12, 32, 2310, 10, 30030, 212, 36, 8, 510510, 14, 9699690, 34, 216, 2312, 223092870, 12, 60, 30032, 18, 214, 6469693230, 38, 200560490130, 10, 2316, 510512, 240, 16, 7420738134810, 9699692, 30036, 36, 304250263527210, 218, 13082761331670030, 2314, 42, 223092872, 614889782588491410, 14

Offset: 1

Author

Antti Karttunen, May 27 2024

Keywords

• nonn

Comments

Completely additive with a(p^e) = e * A002110(A000720(p)).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2048
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. also A000040, A000720, A002110, A003961, A034386, A060389, A108951, A276085, A276154, A373984 [= A108951(n)-a(n)], A373985 [= gcd(a(n), A108951(n))], A373986, A373987.

Programs

PARI

A373158(n) = { my(f=factor(n)); sum(i=1, #f~, f[i, 2]*prod(i=1,primepi(f[i, 1]),prime(i))); }; \\ corrected Jun 25 2024

Formula

From Antti Karttunen, Jun 25 2024, Oct 28 2024: (Start)

a(n) = A276085(A003961(n)).

For n >= 1, a(A000040(n)) = A002110(n), a(A002110(n)) = A060389(n).

(End)

Extensions

Data [first incorrect term was at a(8)] and the faulty PARI-program corrected by Antti Karttunen, Jun 25 2024