A029590 For n>0, a(n) is the least quasi-Carmichael number to base n; a(0) = least composite squarefree integer.

6, 561, 1595, 35, 1705, 77, 13481, 187, 143, 209, 4807, 221, 14807, 493, 20723, 323, 7429, 437, 36593, 943, 713, 989, 1147, 1073, 899, 1537, 1271, 899, 1333, 1517, 104355281, 1591, 1517, 2993, 1591, 1517, 621193, 3397, 1763, 1763, 2623, 2021

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Comments

a(n) is the least squarefree composite integer for which prime p | a(n) ==> p-n | a(n)-n.

Examples

			For n=6 the minimum is a(n)=13481. Prime factors of 13481 are 13, 17 and 61. We have 13481 - 6 = 13475, 13 - 6 = 7 and 13475 / 7 = 1925, 17 - 6 = 11 and 13475 / 11 = 1225, 61 - 6 = 55 and 13475 / 55 = 245. - _Elijah Beregovsky_, Feb 15 2020
		

Links

• Donovan Johnson, Table of n, a(n) for n = 0..500
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Cf. A029591 (base -n), A257750 (quasi-Carmichael numbers).

Programs

Mathematica

qcQ[n_,k_] := Module[{f = FactorInteger[n]}, p = f[[;; , 1]]; e = f[[;; , 2]];om=Length[e]; om>=2 && Max[e] == 1 && Min[p]>k && Length@Select[p, Divisible[n-k, #-k]&] == om]; seq[k_]:=SelectFirst[Range[1,50000], qcQ[#,k]&]; Print[seq/@Range[0,29]]; (* Elijah Beregovsky, Feb 15 2020 *)