A290497 Carmichael numbers with a record number of aliquot divisors that are also Carmichael numbers.

561, 63973, 31146661, 509033161, 84127131361, 11985185775745, 712484043821641, 24349841028259201, 53545320695780641, 141125066711098561, 16223841675726285601, 562477984940049379201

Offset

1,1

Comments

The number of aliquot divisors is 0, 1, 2, 5, 7, 8, 10, 11, 17, 20, 26, 27, ...

The terms were calculated using Pinch's tables of Carmichael numbers (see link below).

Links

Table of n, a(n) for n=1..12.

Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.

R. G. E. Pinch, Tables relating to Carmichael numbers.

Index entries for sequences related to Carmichael numbers.

Example

509033161 is in the sequence since it is a Carmichael number, and 5 of its divisors are also Carmichael numbers (1729, 63973, 126217, 188461 and 294409), more than for any smaller Carmichael number.

Mathematica

A002997 =  Cases[Range[1, 100000, 2], n_ /; Mod[n, CarmichaelLambda[n]] == 1 && ! PrimeQ[n]]; carmichaelQ[n_] := Not[PrimeQ[n]] && Divisible[n - 1, CarmichaelLambda[n]]; numSol[n_] := Module[{m = 0}, ds = Divisors[n];   Do[d = ds[[k]]; If[! carmichaelQ[d], Continue[]]; m++, {k, 2, Length[ds] - 1}]; m]; numSolmax = -1; seq = {}; Do[n = A002997[[j]]; m = numSol[n]; If[m > numSolmax, AppendTo[seq, n]; numSolmax = m], {j, 1, Length[A002997]}]; seq

Crossrefs

Cf. A002997.

Sequence in context: A258801 A329460 A097061 * A258839 A371759 A213867

Adjacent sequences: A290494 A290495 A290496 * A290498 A290499 A290500

Keyword

nonn,more

Author

Amiram Eldar, Aug 04 2017

Extensions

a(11) from Amiram Eldar, Jun 29 2019

a(12) calculated using data from Claude Goutier and added by Amiram Eldar, Apr 24 2024

Status

approved