A354872 a(n) = A056239(n) / gcd(A056239(n), A258851(n)).

1, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 1, 5, 1, 1, 5, 1, 5, 3, 2, 1, 5, 1, 7, 1, 3, 1, 6, 1, 1, 7, 8, 7, 1, 1, 9, 2, 1, 1, 7, 1, 7, 7, 10, 1, 3, 1, 7, 9, 2, 1, 7, 4, 7, 5, 11, 1, 7, 1, 12, 1, 1, 3, 8, 1, 3, 11, 8, 1, 7, 1, 13, 2, 5, 9, 9, 1, 7, 1, 14, 1, 2, 5, 15, 3, 2, 1, 8, 5, 11, 13, 16, 11, 7, 1, 9, 3, 2, 1, 10

Offset: 2

Author

Antti Karttunen, Jun 11 2022

Keywords

• nonn
• frac

Comments

Numerator of fraction A056239(n) / A258851(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 2..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A056239, A258851, A278510, A354871, A354873 (denominators).

Programs

PARI

A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
A258851(n) = (n*sum(i=1, #n=factor(n)~, n[2, i]*primepi(n[1, i])/n[1, i])); \\ From A258851
A354872(n) = { my(u=A056239(n)); (u/gcd(u, A258851(n))); };
\\ Or:
A354872(n) = numerator(A056239(n)/A258851(n));

Formula

a(n) = A056239(n) / A354871(n) = A056239(n) / gcd(A056239(n), A258851(n)).