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

0,1

Comments

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

Links

Donovan Johnson, Table of n, a(n) for n = 0..500

Index entries for sequences related to Carmichael numbers.

Example

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

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 *)

Crossrefs

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

Sequence in context: A358487 A341871 A226263 * A332156 A291953 A225206

Adjacent sequences: A029587 A029588 A029589 * A029591 A029592 A029593

Keyword

nonn

Author

David W. Wilson

Status

approved