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

Author

Shyam Sunder Gupta, Nov 03 2013

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

PARI

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