A373987 Denominator 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).

1, 1, 1, 1, 1, 3, 1, 4, 3, 15, 1, 12, 1, 105, 5, 2, 1, 36, 1, 60, 35, 1155, 1, 4, 15, 15015, 12, 420, 1, 180, 1, 16, 1155, 255255, 105, 9, 1, 4849845, 15015, 20, 1, 1260, 1, 4620, 180, 111546435, 1, 48, 105, 900, 85085, 60060, 1, 108, 385, 70, 1616615, 3234846615, 1, 18, 1, 100280245065, 1260, 16, 5005, 13860, 1, 1021020

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, A373986 (numerators).

Programs

PARI

A373987(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]); m/gcd(m,s); };

PARI

A373987(n) = denominator(A373158(n)/A108951(n));

Formula

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