A202159 - OEIS

A202159

a(n) = smallest k having at least four prime divisors d such that (d + n) | (k + n).

8855, 11590, 27885, 122360, 16555, 10290, 6545, 61642, 71799, 65195, 14245, 142788, 63635, 580930, 39585, 21098, 69003, 258482, 59885, 378952, 8715, 266090, 133285, 690501, 27335, 704790, 1017423, 299222, 187891, 771650, 293405, 1638598, 282315, 553610, 227205

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OFFSET

1,1

COMMENTS

The sequence of numbers k composite and squarefree, prime p | k ==> p+n | k+n is given by A029591 (least quasi-Carmichael number of order -n).

If k is squarefree, for n = 1, we obtain Lucas-Carmichael numbers: A006972.

In this sequence, the majority of terms are not squarefree.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..450

EXAMPLE

a(3) = 27885 because the prime divisors of 27885 are 3, 5, 11, 13 =>

(3 + 3)| (27885 + 3) = 27888 = 6*4648;

(5 + 3) | 27888 = 8*3486;

(11 + 3) | 27888 = 14*1992;

(13 + 3) | 27888 = 16*1743.

MAPLE

with(numtheory):for n from 1 to 33 do:i:=0:for k from 1 to 5000000 while(i=0) do:x:=factorset(k):n1:=nops(x):y:=k+n: j:=0:for m from 1 to n1 do:if n1>=2 and irem(y, x[m]+n)=0 then j:=j+1:else fi:od:if j>3 then i:=1:printf(`%d, `, k):else fi:od:od:

MATHEMATICA

numd[n_, k_] := Module[{p=FactorInteger[k][[;; , 1]], c=0}, Do[If[Divisible[n+k, n+p[[i]]], c++], {i, 1, Length[p]}]; c]; a[n_]:=Module[{k=1}, While[numd[n, k] <= 3, k++]; k]; Array[a, 35] (* Amiram Eldar, Sep 09 2019 *)

CROSSREFS

Cf. A006972, A029591, A202157, A202158.

Sequence in context: A250010 A064296 A031797 * A216926 A292572 A236031

Adjacent sequences: A202156 A202157 A202158 * A202160 A202161 A202162

KEYWORD

nonn

AUTHOR

Michel Lagneau, Dec 13 2011

STATUS

approved