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Smallest sets of 6 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.
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%I #5 Nov 13 2013 15:05:22

%S 2987,4727,9723,18843,22983,30543,35147,39947,45047,50463,55787,56807,

%T 58055,58779,69183,78047,81947,85743,101147,106143,108255,109247,

%U 117123,134087,139743,139803,152567,171287,174347,175907,182643,189767,197027,199803,202127

%N Smallest sets of 6 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.

%H Shyam Sunder Gupta, <a href="/A231628/b231628.txt">Table of n, a(n) for n = 1..5000</a>

%e 2987, 2989, 2991, 2993, 2995, 2997 is the smallest set of 6 consecutive deficient numbers in arithmetic progression so 2987 is in the list.

%t DefQ[n_] := DivisorSigma[1, n] < 2 n; m = 2; z1 = 2; cd = 1; a = {}; Do[If[DefQ[n], If[n - z1 == cd, m = m + 1; If[m > 5, AppendTo[a, n - 5*cd]], m = 2; cd = n - z1]; z1 = n], {n, 3, 1000000}]; a

%Y Cf. A005100, A231623, A228963, A231624, A231625, A231626.

%K nonn

%O 1,1

%A _Shyam Sunder Gupta_, Nov 11 2013