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.

A353868 Numbers k such that the Carmichael function A002322(k) divides Dedekind psi A001615(k).

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 12, 14, 15, 16, 18, 20, 24, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 52, 54, 56, 60, 63, 64, 65, 70, 72, 75, 78, 80, 81, 84, 90, 96, 98, 100, 104, 105, 108, 112, 117, 119, 120, 126, 128, 130, 135, 140, 144, 150, 156, 160, 162, 168, 175, 180, 182, 189, 190, 192, 195, 196, 200, 204, 208, 210, 216
Offset: 1

Views

Author

Max Alekseyev, May 08 2022

Keywords

Comments

If coprime s,t are terms, then so is s*t. Also, if t is a term and prime p|t, then p*t is also a term. Squarefree terms are listed in A353869, primitive terms are listed in A353870, and their intersection forms A353871.

Links

Crossrefs

Cf. A002322, A001615, A353869, A353870, A353871.

Programs

  • Mathematica
    psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); Select[Range[216], Divisible[psi[#], CarmichaelLambda[#]] &] (* Amiram Eldar, May 09 2022 *)

A353869 Squarefree numbers k such that the Carmichael function A002322(k) divides the Dedekind psi A001615(k).

Original entry on oeis.org

1, 2, 3, 6, 14, 15, 30, 35, 42, 65, 70, 78, 105, 119, 130, 182, 190, 195, 210, 238, 255, 357, 370, 377, 390, 418, 455, 510, 546, 570, 595, 663, 714, 754, 910, 969, 1045, 1110, 1118, 1131, 1190, 1254, 1326, 1330, 1365, 1547, 1558, 1615, 1785, 1885, 1887, 1938, 2090, 2190, 2261, 2262, 2470, 2590, 2639, 2730
Offset: 1

Views

Author

Max Alekseyev, May 08 2022

Keywords

Comments

If s,t are terms, then so is lcm(s,t); in particular, if s,t are coprime, then s*t is also a term. Primitive squarefree terms are listed in A353871.

Crossrefs

Intersection of A005117 and A353868.
Cf. A002322, A001615, A353870, A353871.

Programs

  • Mathematica
    psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); Select[Range[3000], SquareFreeQ[#] && Divisible[psi[#], CarmichaelLambda[#]] &] (* Amiram Eldar, May 09 2022 *)

A353870 Primitive terms of A353868.

Original entry on oeis.org

1, 2, 3, 14, 15, 20, 35, 52, 63, 65, 78, 117, 119, 182, 190, 204, 255, 272, 275, 342, 370, 377, 418, 455, 513, 595, 663, 666, 680, 775, 819, 855, 969, 999, 1045, 1118, 1292, 1314, 1330, 1421, 1460, 1525, 1547, 1558, 1615, 1665, 1768, 1881, 1885, 1887, 1925, 1971, 2190, 2261, 2328, 2394, 2470, 2590, 2639, 2716
Offset: 1

Views

Author

Max Alekseyev, May 08 2022

Keywords

Comments

Terms of A353868 that are neither a product of smaller terms nor a product of a term and a prime dividing it.

Crossrefs

Squarefree terms form A353871.
Cf. A002322, A001615, A353868, A353869.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.