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.

A292571 Lucas-Carmichael numbers whose Dedekind psi value is a square.

Original entry on oeis.org

935, 31535, 76751, 1707839, 3106799, 11141999, 24685199, 43383167, 83618639, 151524071, 161841239, 189099039, 212133599, 213884999, 219155615, 233743319, 241485839, 271038599, 287432495, 338340239, 353107799, 624840479, 660423455, 945236159, 1171355471
Offset: 1

Views

Author

Amiram Eldar, Sep 19 2017

Keywords

Examples

			psi(935) = 36^2.
		

Crossrefs

Intersection of A006972 and A291167.

Programs

  • Mathematica
    psi[n_] := If[n < 1, 0, n*Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]]; s = Import["b006972.txt","Data"][[All,-1]]; Select[s, IntegerQ@Sqrt[psi@#] &]

A292572 Lucas-Carmichael numbers whose Dedekind psi value is a cube.

Original entry on oeis.org

8855, 31535, 73535, 265895, 12676799, 30071327, 86450399, 561645839, 674628479, 741722399, 945066527, 1066699799, 1304305415, 2239506719, 2423951999, 2693338559, 3512071871, 4708417055, 4811496767, 8194093919, 9140299199, 9184665599, 9405512639, 11729537855
Offset: 1

Views

Author

Amiram Eldar, Sep 19 2017

Keywords

Examples

			psi(8855) = 24^3.
		

Crossrefs

Programs

  • Mathematica
    psi[n_] := If[n < 1, 0, n*Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]]; s = Import["b006972.txt","Data"][[All,-1]];Select[s, IntegerQ@Power[psi@#, 1/3] &]

A290805 Least Carmichael number whose Euler totient function value is an n-th power.

Original entry on oeis.org

561, 1729, 63973, 1729, 367939585, 63973, 294409, 232289960085001, 11570858964626401, 79939760257, 509033161, 611559276803883001, 13079177569, 27685385948423487745, 26979791457662785, 287290964059686145, 13046319747121261903830001, 7847507962539316696504321, 993942550111105, 6280552422566791778305, 24283361157780097, 759608966313690599499265, 6657107145346817668085761, 283219223388059484626764342346640001
Offset: 1

Views

Author

Amiram Eldar, Aug 11 2017

Keywords

Comments

Banks proved that for each positive integer N there are an infinite number of Carmichael numbers whose Euler totient function value is an N-th power. Therefore this sequence is infinite.
For any n > 26, a(n) > 10^22. - Amiram Eldar, Apr 20 2024

Examples

			phi(1729) = 36^2 = 6^4 while phi(561) and phi(1105) are not perfect powers, therefore a(2) = a(4) = 1729.
		

Crossrefs

Extensions

Terms up to a(13) were calculated using Pinch's tables of Carmichael numbers.
a(1) prepended by David A. Corneth, Aug 11 2017
a(14)-a(16), a(19)-a(21), a(25)-a(26) calculated using data from Claude Goutier and added by Amiram Eldar, Apr 20 2024
a(17)-a(18), a(22)-a(24) from Max Alekseyev, Apr 25 2024
Edited by Max Alekseyev, Dec 04 2024
Showing 1-3 of 3 results.