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

1,2

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

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)

Prog

(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

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.

Sequence in context: A326579 A057643 A073039 * A322792 A253588 A228099

Adjacent sequences: A373155 A373156 A373157 * A373159 A373160 A373161

Keyword

nonn

Author

Antti Karttunen, May 27 2024

Extensions

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

Status

approved