A231088 Initial members of abundant triples, i.e., values of k such that (k, k+2, k+4) are all abundant numbers.

100, 196, 220, 304, 348, 350, 364, 460, 616, 640, 700, 736, 832, 1036, 1060, 1144, 1180, 1216, 1312, 1372, 1456, 1480, 1660, 1696, 1876, 1900, 1936, 1984, 1998, 2000, 2020, 2176, 2208, 2210, 2296, 2320, 2548, 2620, 2716, 2740, 2748, 2750, 2988, 2990, 2992

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Shyam Sunder Gupta)

Example

100, 102, 104 are abundant, thus the smallest number is listed.

Mathematica

AbundantQ[n_] := DivisorSigma[1, n] > 2n; m = 0; a = {}; Do[If[AbundantQ[n], m = m + 1; If[m > 2, AppendTo[a, n - 4]], m = 0], {n, 2, 1000000, 2}]; a
2*Flatten[Position[Partition[Table[If[DivisorSigma[1, n]>2n, 1, 0], {n, 2, 3000, 2}], 3, 1], {1, 1, 1}]] (* Harvey P. Dale, Aug 19 2014 *)
2*SequencePosition[Table[If[DivisorSigma[1, n]>2n, 1, 0], {n, 2, 3000, 2}], {1, 1, 1}][[;; , 1]] (* Harvey P. Dale, Feb 27 2023 *)

Prog

(PARI) is(n)=sigma(n, -1)>2 && sigma(n+2, -1)>2 && sigma(n+4, -1)>2 \\ Charles R Greathouse IV, Feb 21 2017

Crossrefs

Cf. A005101, A096399, A108926, A231086, A231089, A231090, A231092, A231093.

Sequence in context: A025408 A068805 A369417 * A365745 A104023 A072367

Adjacent sequences: A231085 A231086 A231087 * A231089 A231090 A231091

Keyword

nonn

Author

Shyam Sunder Gupta, Nov 03 2013

Status

approved