A228964 Smallest sets of 7 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.

1242, 6702, 7962, 12162, 13842, 15522, 16362, 18042, 18882, 19722, 24762, 26442, 27282, 27702, 28122, 28962, 36942, 38202, 39462, 43662, 44922, 45762, 48282, 48702, 51222, 55842, 56682, 60042, 62562, 63402, 66762, 69282, 69702, 70962, 71802, 73062, 73482

Offset: 1

Author

Shyam Sunder Gupta, Nov 10 2013

Keywords

• nonn

Examples

			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.
		

Links

• Shyam Sunder Gupta, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A005101, A228433, A228844, A228961, A228962, A228963.

Programs

Mathematica

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
Select[Partition[Select[Range[80000],DivisorSigma[1,#]>2#&],7,1], Length[ Union[ Differences[#]]] ==1&][[All,1]] (* Harvey P. Dale, Oct 15 2017 *)