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

1,1

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A028514 A099178 A209711 * A047628 A181073 A023065

Adjacent sequences: A228961 A228962 A228963 * A228965 A228966 A228967

Keyword

nonn

Author

Shyam Sunder Gupta, Nov 10 2013

Status

approved