cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A342449 a(n) = Sum_{k=1..n} gcd(k,n)^k.

Original entry on oeis.org

1, 5, 29, 262, 3129, 46705, 823549, 16777544, 387421251, 10000003469, 285311670621, 8916100581446, 302875106592265, 11112006826387025, 437893890391180013, 18446744073743123788, 827240261886336764193, 39346408075299116257065
Offset: 1

Views

Author

Seiichi Manyama, Mar 13 2021

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := Sum[GCD[k, n]^k, {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 13 2021 *)
  • PARI
    a(n) = sum(k=1, n, gcd(k, n)^k);

Formula

If p is prime, a(p) = p-1 + p^p = A231712(p).

A342394 a(n) = Sum_{k=1..n} k^(gcd(k,n) - 1).

Original entry on oeis.org

1, 3, 11, 68, 629, 7793, 117655, 2097228, 43046772, 1000000649, 25937424611, 743008379146, 23298085122493, 793714773371841, 29192926025401528, 1152921504608945960, 48661191875666868497, 2185911559738739835591, 104127350297911241532859
Offset: 1

Views

Author

Seiichi Manyama, Mar 10 2021

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := Sum[k^(GCD[k, n] - 1), {k, 1, n}]; Array[a, 19] (* Amiram Eldar, Mar 10 2021 *)
  • PARI
    a(n) = sum(k=1, n, k^(gcd(k, n)-1));

Formula

If p is prime, a(p) = p-1 + p^(p-1) = A173235(p) = A056665(p).

A342395 a(n) = Sum_{k=1..n} k^(n/gcd(k,n)).

Original entry on oeis.org

1, 3, 12, 90, 1305, 15713, 376768, 6163324, 176787369, 3769360335, 142364319636, 3152514811878, 154718778284161, 4340009168261557, 210971169749009040, 7281661102087491416, 435659030617933827153, 14181101408651996188995
Offset: 1

Views

Author

Seiichi Manyama, Mar 10 2021

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := Sum[k^(n/GCD[k, n]), {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Mar 10 2021 *)
  • PARI
    a(n) = sum(k=1, n, k^(n/gcd(k, n)));

Formula

If p is prime, a(p) = A121706(p) + p.
Showing 1-3 of 3 results.