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.
%I A287840 #14 Sep 03 2017 22:05:37
%S A287840 36,48,60,72,80,108,112,120,144,180,198,216,224,240,252,288,300,324,
%T A287840 336,360,396,420,432,468,480,504,528,540,560,576,594,600,612,630,648,
%U A287840 660,672,720,756,768,780,792,810,828,840,864,900,936,960,972,990,1008
%N A287840 Numbers that generate Carmichael numbers using Erdős's method.
%C A287840 Erdős showed in 1956 how to construct Carmichael numbers from a given number n (typically with many divisors). Given a number n, let P be the set of primes p such that (p-1)|n but p is not a factor of n. Let c be a product of a subset of P with at least 3 elements. If c == 1 (mod n) then c is a Carmichael number.
%C A287840 Numbers with only one generated Carmichael number: 48, 80, 224, 252, 324, 468, 528, 560, 594, 780, 972, 1104, 1232, 1368, 1536, 1848, 2024, ...
%H A287840 Paul Erdős, <a href="https://renyi.hu/~p_erdos/1956-10.pdf">On pseudoprimes and Carmichael numbers</a>, Publ. Math. Debrecen 4 (1956), pp. 201-206.
%H A287840 Andrew Granville, <a href="http://www.dms.umontreal.ca/~andrew/PDF/Notices1.pdf">Primality testing and Carmichael numbers</a>, Notices of the American Mathematical Society, Vol. 39 No. 6 (1992), pp. 696-700.
%H A287840 Andrew Granville and Carl Pomerance, <a href="https://doi.org/10.1090/S0025-5718-01-01355-2">Two contradictory conjectures concerning Carmichael numbers</a>, Mathematics of Computation, Vol. 71, No. 238 (2002), pp. 883-908.
%e A287840 The set of primes for n = 36 is P={5, 7, 13, 19, 37}. Two subsets, {7, 13, 19} and {7, 13, 19, 37} have c == 1 (mod n): c = 7*13*19 = 1729 and c = 7*13*19*37 = 63973. 36 is the first number that generates Carmichael numbers thus a(1)=36.
%t A287840 a = {}; Do[p = Select[Divisors[n] + 1, PrimeQ]; pr = Times @@ p; pr = pr/GCD[n, pr]; ps = Divisors[pr]; c = 0; Do[p1 = FactorInteger[ps[[j]]][[;; , 1]]; If[Length[p1] < 3, Continue[]]; c1 = Times @@ p1; If[Mod[c1, n] == 1, c++], {j, 1, Length[ps]}]; If[c > 0, AppendTo[a, n]], {n, 1, 1000}]; a
%Y A287840 Cf. A002997.
%K A287840 nonn
%O A287840 1,1
%A A287840 _Amiram Eldar_, Sep 01 2017