A231088 - OEIS

%I #25 Apr 06 2024 07:53:40

%S 100,196,220,304,348,350,364,460,616,640,700,736,832,1036,1060,1144,

%T 1180,1216,1312,1372,1456,1480,1660,1696,1876,1900,1936,1984,1998,

%U 2000,2020,2176,2208,2210,2296,2320,2548,2620,2716,2740,2748,2750,2988,2990,2992

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

%H Amiram Eldar, <a href="/A231088/b231088.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from Shyam Sunder Gupta)

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

%t 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

%t 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 *)

%t 2*SequencePosition[Table[If[DivisorSigma[1,n]>2n,1,0],{n,2,3000,2}],{1,1,1}][[;;,1]] (* _Harvey P. Dale_, Feb 27 2023 *)

%o (PARI) is(n)=sigma(n,-1)>2 && sigma(n+2,-1)>2 && sigma(n+4,-1)>2 \\ _Charles R Greathouse IV_, Feb 21 2017

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

%K nonn

%O 1,1

%A _Shyam Sunder Gupta_, Nov 03 2013