cp's OEIS Frontend

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

%I A290497 #19 Apr 24 2024 02:42:23
%S A290497 561,63973,31146661,509033161,84127131361,11985185775745,
%T A290497 712484043821641,24349841028259201,53545320695780641,
%U A290497 141125066711098561,16223841675726285601,562477984940049379201
%N A290497 Carmichael numbers with a record number of aliquot divisors that are also Carmichael numbers.
%C A290497 The number of aliquot divisors is 0, 1, 2, 5, 7, 8, 10, 11, 17, 20, 26, 27, ...
%C A290497 The terms were calculated using Pinch's tables of Carmichael numbers (see link below).
%H A290497 Claude Goutier, <a href="http://www-labs.iro.umontreal.ca/~goutier/OEIS/A055553/">Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22</a>.
%H A290497 R. G. E. Pinch, <a href="http://s369624816.websitehome.co.uk/rgep/carpsp.html">Tables relating to Carmichael numbers</a>.
%H A290497 <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%e A290497 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.
%t A290497 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
%Y A290497 Cf. A002997.
%K A290497 nonn,more
%O A290497 1,1
%A A290497 _Amiram Eldar_, Aug 04 2017
%E A290497 a(11) from _Amiram Eldar_, Jun 29 2019
%E A290497 a(12) calculated using data from _Claude Goutier_ and added by _Amiram Eldar_, Apr 24 2024