A373158 - OEIS

%I #21 Oct 28 2024 16:23:32

%S 0,2,6,4,30,8,210,6,12,32,2310,10,30030,212,36,8,510510,14,9699690,34,

%T 216,2312,223092870,12,60,30032,18,214,6469693230,38,200560490130,10,

%U 2316,510512,240,16,7420738134810,9699692,30036,36,304250263527210,218,13082761331670030,2314,42,223092872,614889782588491410,14

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

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

%H Antti Karttunen, <a href="/A373158/b373158.txt">Table of n, a(n) for n = 1..2048</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F From _Antti Karttunen_, Jun 25 2024, Oct 28 2024: (Start)

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

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

%F (End)

%o (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

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

%K nonn

%O 1,2

%A _Antti Karttunen_, May 27 2024

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