A231089 Initial members of abundant quadruplets, i.e., values of k such that (k, k+2, k+4, k+6) are all abundant numbers.

348, 1998, 2208, 2748, 2988, 2990, 3006, 3246, 3708, 3846, 4506, 4728, 4730, 5166, 6228, 7068, 7206, 7908, 8886, 9348, 9588, 9724, 9726, 11406, 13746, 14208, 14766, 17148, 17988, 18126, 18588, 18828, 18844, 18846, 19548, 20148, 20478, 21486, 22188, 22984

Offset

1,1

Links

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

Example

348, 350, 352, 354 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 > 3, AppendTo[a, n - 6]], m = 0], {n, 2, 1000000, 2}]; a
SequencePosition[Table[If[DivisorSigma[1, n]>2n, 1, 0], {n, 23000}], {1, _, 1, _, 1, _, 1}][[All, 1]] (* Harvey P. Dale, Apr 02 2018 *)

Prog

(PARI) is(n)=sigma(n, -1)>2 && sigma(n+2, -1)>2 && sigma(n+4, -1)>2 && sigma(n+6, -1)>2 \\ Charles R Greathouse IV, Feb 21 2017

Crossrefs

Cf. A005101, A096399, A108926, A231086, A231088, A231090, A231092, A231093.

Sequence in context: A275237 A129642 A304837 * A237318 A237724 A054467

Adjacent sequences: A231086 A231087 A231088 * A231090 A231091 A231092

Keyword

nonn

Author

Shyam Sunder Gupta, Nov 03 2013

Status

approved