A340078 -id:A340078 - cp's OEIS frontend

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

Antti Karttunen, Dec 30 2020

nonn

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

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

Cf. A018804, A340078, A340080.

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

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

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

A340080 a(n) = (1+A018804(n)) / gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).

Original entry on oeis.org

2, 2, 2, 9, 2, 8, 2, 21, 22, 14, 2, 41, 2, 20, 46, 49, 2, 32, 2, 73, 22, 32, 2, 101, 66, 38, 82, 15, 2, 68, 2, 113, 106, 50, 118, 169, 2, 56, 42, 181, 2, 14, 2, 169, 38, 68, 2, 241, 134, 98, 166, 201, 2, 122, 38, 261, 62, 86, 2, 361, 2, 92, 274, 257, 226, 158, 2, 265, 226, 176, 2, 421, 2, 110, 326, 297, 274, 188

Offset: 1

Antti Karttunen, Dec 31 2020

nonn

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

Cf. A018804, A340078, A340079.

A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
A340080(n) = { my(x=1+A018804(n)); x/gcd(n,x); };

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

cp's OEIS Frontend

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

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