A340079 a(n) = n / gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).

1, 1, 1, 4, 1, 3, 1, 8, 9, 5, 1, 12, 1, 7, 15, 16, 1, 9, 1, 20, 7, 11, 1, 24, 25, 13, 27, 4, 1, 15, 1, 32, 33, 17, 35, 36, 1, 19, 13, 40, 1, 3, 1, 44, 9, 23, 1, 48, 49, 25, 51, 52, 1, 27, 11, 56, 19, 29, 1, 60, 1, 31, 63, 64, 65, 33, 1, 68, 69, 35, 1, 72, 1, 37, 75, 76, 77, 39, 1, 80, 81, 41, 1, 84, 85, 43, 87, 88

Offset: 1

Author

Antti Karttunen, Dec 30 2020

Keywords

• nonn

Comments

It is conjectured that this is 1 iff n is 1 or a prime. See Thomas Ordowski's Oct 22 2014 comment in A018804.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A018804, A340078, A340080.

Cf. also A055032, A323072 (similar but different sequences).

Programs

PARI

A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
A340079(n) = (n/gcd(n,1+A018804(n)));

Formula

a(n) = n / A340078(n) = n / gcd(n, 1+A018804(n)).