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 *)

A353871 Squarefree primitive terms of A353868; also primitive terms of A353869.

Original entry on oeis.org

1, 2, 3, 14, 15, 35, 65, 78, 119, 182, 190, 255, 370, 377, 418, 455, 595, 663, 969, 1045, 1118, 1330, 1547, 1558, 1615, 1885, 1887, 2190, 2261, 2470, 2590, 2639, 2795, 2926, 3315, 3395, 3553, 3567, 3723, 3895, 4074, 4147, 4199, 4403, 4407, 4810, 5110, 5434, 5890, 5945, 7030, 7315, 7826, 8106, 8323, 8569
Offset: 1

Views

Author

Max Alekseyev, May 08 2022

Keywords

Comments

Terms of A353869 that cannot be obtained as a product of smaller terms.

Crossrefs

Intersection of A353869 and A353870. Also, intersection of A005117 and A353870.
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.

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