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A029590 For n>0, a(n) is the least quasi-Carmichael number to base n; a(0) = least composite squarefree integer. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A213959 A341871 A226263 * A332156 A291953 A225206

Adjacent sequences:  A029587 A029588 A029589 * A029591 A029592 A029593

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified February 27 11:38 EST 2021. Contains 341656 sequences. (Running on oeis4.)