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%I #10 Oct 15 2017 19:08:17
%S 1242,6702,7962,12162,13842,15522,16362,18042,18882,19722,24762,26442,
%T 27282,27702,28122,28962,36942,38202,39462,43662,44922,45762,48282,
%U 48702,51222,55842,56682,60042,62562,63402,66762,69282,69702,70962,71802,73062,73482
%N Smallest sets of 7 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.
%H Shyam Sunder Gupta, <a href="/A228964/b228964.txt">Table of n, a(n) for n = 1..5000</a>
%e 1242, 1248, 1254, 1260, 1266, 1272, 1278 is the smallest set of 7 consecutive abundant numbers in arithmetic progression so 1242 is in the list.
%t AbundantQ[n_] := DivisorSigma[1, n] > 2 n; m = 2; z1 = 18; cd = 6; a = {}; Do[If[AbundantQ[n], If[n - z1 == cd, m = m + 1; If[m > 6, AppendTo[a, n - 6*cd]], m = 2; cd = n - z1]; z1 = n], {n, 19, 1000000}]; a
%t Select[Partition[Select[Range[80000],DivisorSigma[1,#]>2#&],7,1], Length[ Union[ Differences[#]]] ==1&][[All,1]] (* _Harvey P. Dale_, Oct 15 2017 *)
%Y Cf. A005101, A228433, A228844, A228961, A228962, A228963.
%K nonn
%O 1,1
%A _Shyam Sunder Gupta_, Nov 10 2013
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