A373986 Numerator of A373158(n) / A108951(n), where A108951 is fully multiplicative and A373158 is fully additive with a(p) = p# for prime p, where x# is the primorial A034386(x).

0, 1, 1, 1, 1, 2, 1, 3, 1, 8, 1, 5, 1, 53, 1, 1, 1, 7, 1, 17, 6, 578, 1, 1, 1, 7508, 1, 107, 1, 19, 1, 5, 193, 127628, 4, 1, 1, 2424923, 2503, 3, 1, 109, 1, 1157, 7, 55773218, 1, 7, 1, 31, 14181, 15017, 1, 5, 13, 9, 269436, 1617423308, 1, 1, 1, 50140122533, 37, 3, 167, 1159, 1, 255257, 18591073, 121, 1, 1, 1, 1855184533703

Offset: 1

Author

Antti Karttunen, Jun 25 2024

Keywords

• nonn
• frac

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A108951, A373158, A373985, A373987 (denominators), A373988 (rgs-transform).

Programs

PARI

A373986(n) = { my(f=factor(n),m=1,s=0); for(i=1, #f~, my(x=prod(i=1,primepi(f[i, 1]),prime(i))); s += f[i, 2]*x; m *= x^f[i, 2]); s/gcd(m,s); };

PARI

A373986(n) = numerator(A373158(n)/A108951(n));

Formula

a(n) = A373158(n) / A373985(n) = A373158(n) / gcd(A108951(n), A373158(n)).