login
A231088
Initial members of abundant triples, i.e., values of k such that (k, k+2, k+4) are all abundant numbers.
8
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
KEYWORD
nonn
AUTHOR
Shyam Sunder Gupta, Nov 03 2013
STATUS
approved