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Smallest sets of 8 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.
0

%I #8 Apr 10 2021 06:02:13

%S 221355125,221355127,402640539,402640541,668862579,668862581,

%T 739577139,739577141

%N Smallest sets of 8 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.

%e 221355125, 221355127, 221355129, 221355131, 221355133, 221355135, 221355137, 221355139 is the smallest set of 8 consecutive deficient numbers in arithmetic progression so 221355125 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 > 7, AppendTo[a, n - 7*cd]], m = 2; cd = n - z1]; z1 = n], {n, 3, 1000000000}]; a

%Y Cf. A005100, A231623, A228965, A231624, A231625, A231626, A231628, A231629.

%K nonn

%O 1,1

%A _Shyam Sunder Gupta_, Nov 11 2013