A354987 -id:A354987 - cp's OEIS frontend

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

1, 1, 2, 3, 4, 2, 6, 7, 8, 4, 10, 3, 12, 6, 1, 15, 16, 8, 18, 4, 6, 10, 22, 2, 24, 12, 26, 1, 28, 1, 30, 31, 1, 16, 2, 8, 36, 18, 12, 1, 40, 6, 42, 1, 1, 22, 46, 15, 48, 24, 1, 12, 52, 26, 10, 7, 18, 28, 58, 3, 60, 30, 3, 63, 1, 1, 66, 16, 1, 2, 70, 8, 72, 36, 24, 1, 3, 12, 78, 15, 80, 40, 82, 4, 2, 42, 1, 2, 88

Offset: 1

Antti Karttunen, Jun 16 2022

nonn

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, A354986, A354987.

Cf. also A345992.

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_] := GCD[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
A354985(n) = gcd(A047994(n), A344005(n));

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

a(n) = gcd(A047994(n), A346607(n)) = gcd(A344005(n), A346607(n)).

A354986 a(n) = A047994(n) / gcd(A047994(n), A344005(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 8, 1, 1, 1, 1, 3, 2, 1, 1, 7, 1, 1, 1, 18, 1, 8, 1, 1, 20, 1, 12, 3, 1, 1, 2, 28, 1, 2, 1, 30, 32, 1, 1, 2, 1, 1, 32, 3, 1, 1, 4, 6, 2, 1, 1, 8, 1, 1, 16, 1, 48, 20, 1, 3, 44, 12, 1, 7, 1, 1, 2, 54, 20, 2, 1, 4, 1, 1, 1, 9, 32, 1, 56, 35, 1, 32, 72, 66, 2, 1, 72, 31, 1, 1, 20

Offset: 1

Antti Karttunen, Jun 16 2022

Numerator 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, A346608 (positions of terms > 1), A354928 (positions of 1's), A354985, A354987 (denominators).

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_] := Numerator[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
A354986(n) = { my(u=A047994(n)); (u/gcd(u, A344005(n))); };

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

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula