A345999 -id:A345999 - cp's OEIS frontend

A345998 a(n) = m/gcd(m,n), where m = A344005(n).

1, 1, 2, 3, 4, 1, 6, 7, 8, 2, 10, 1, 12, 3, 1, 15, 16, 4, 18, 1, 2, 5, 22, 1, 24, 6, 26, 1, 28, 1, 30, 31, 1, 8, 2, 2, 36, 9, 4, 3, 40, 1, 42, 1, 1, 11, 46, 5, 48, 12, 1, 3, 52, 13, 2, 1, 6, 14, 58, 1, 60, 15, 3, 63, 5, 1, 66, 4, 1, 1, 70, 1, 72, 18, 8, 1, 3, 2, 78, 3, 80, 20, 82

Offset: 1

Robert Dougherty-Bliss and N. J. A. Sloane, Jul 18 2021

nonn

This is A344005(n)/A345992(n).

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Cf. A344005, A345992-A345999.

A354987 a(n) = A344005(n) / gcd(A047994(n), A344005(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 7, 1, 5, 1, 1, 11, 1, 7, 1, 1, 1, 1, 15, 1, 1, 1, 11, 9, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 9, 1, 25, 11, 1, 1, 23, 7, 1, 1, 1, 1, 1, 19, 7, 1, 1, 1, 1, 1, 1, 5, 17, 1, 29, 16, 1, 9, 13, 23, 1, 1, 19, 16, 1, 1, 11, 1, 1, 17

Offset: 1

Antti Karttunen, Jun 16 2022

Denominator of fraction A047994(n) / A344005(n).

Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A047994, A344005, A346607, A354985, A354986 (numerators).

Cf. also A345998, A345999.

s[n_] := Module[{m = 1}, While[!Divisible[m*(m + 1), n], m++]; m]; f[p_, e_] := p^e - 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; uphi[1] = 1; a[n_] := Denominator[uphi[n]/s[n]]; Array[a, 100] (* Amiram Eldar, Jun 16 2022 *)

A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
A354987(n) = { my(u=A344005(n)); (u/gcd(u, A047994(n))); };

a(n) = A344005(n) / A354985(n) = A344005(n) / gcd(A047994(n), A344005(n)).

cp's OEIS Frontend

A345998 a(n) = m/gcd(m,n), where m = A344005(n).

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A354987 a(n) = A344005(n) / gcd(A047994(n), A344005(n)).

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