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Numbers with at least one arithmetic progression of four consecutive divisors.
2

%I #8 Feb 24 2019 02:13:32

%S 12,24,36,48,60,72,84,96,105,108,120,132,144,156,168,180,192,204,216,

%T 228,240,252,264,276,288,300,312,315,324,336,348,360,372,384,396,408,

%U 420,432,444,456,468,480,492,504,516,525,528,540,552,564,576,588,600

%N Numbers with at least one arithmetic progression of four consecutive divisors.

%C Contrast A094529 where the divisors in arithmetic progression do not have to be consecutive.

%H Harvey P. Dale, <a href="/A270571/b270571.txt">Table of n, a(n) for n = 1..1000</a>

%e 348 is included because its divisors are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, and 348, and the first four are in arithmetic progression.

%t ap4dQ[n_]:=Count[Partition[Divisors[n],4,1],_?(Length[ Union[ Differences[ #]]] == 1&)]>0; Select[ Range[700],ap4dQ]

%Y Cf. A091011, A094529, A094530.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Mar 19 2016

%E Edited by _Harvey P. Dale_ and _Alois P. Heinz_, Mar 19 2016