A228964
Smallest sets of 7 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.
Original entry on oeis.org
1242, 6702, 7962, 12162, 13842, 15522, 16362, 18042, 18882, 19722, 24762, 26442, 27282, 27702, 28122, 28962, 36942, 38202, 39462, 43662, 44922, 45762, 48282, 48702, 51222, 55842, 56682, 60042, 62562, 63402, 66762, 69282, 69702, 70962, 71802, 73062, 73482
Offset: 1
1242, 1248, 1254, 1260, 1266, 1272, 1278 is the smallest set of 7 consecutive abundant numbers in arithmetic progression so 1242 is in the list.
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AbundantQ[n_] := DivisorSigma[1, n] > 2 n; m = 2; z1 = 18; cd = 6; a = {}; Do[If[AbundantQ[n], If[n - z1 == cd, m = m + 1; If[m > 6, AppendTo[a, n - 6*cd]], m = 2; cd = n - z1]; z1 = n], {n, 19, 1000000}]; a
Select[Partition[Select[Range[80000],DivisorSigma[1,#]>2#&],7,1], Length[ Union[ Differences[#]]] ==1&][[All,1]] (* Harvey P. Dale, Oct 15 2017 *)
A231628
Smallest sets of 6 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.
Original entry on oeis.org
2987, 4727, 9723, 18843, 22983, 30543, 35147, 39947, 45047, 50463, 55787, 56807, 58055, 58779, 69183, 78047, 81947, 85743, 101147, 106143, 108255, 109247, 117123, 134087, 139743, 139803, 152567, 171287, 174347, 175907, 182643, 189767, 197027, 199803, 202127
Offset: 1
2987, 2989, 2991, 2993, 2995, 2997 is the smallest set of 6 consecutive deficient numbers in arithmetic progression so 2987 is in the list.
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DefQ[n_] := DivisorSigma[1, n] < 2 n; m = 2; z1 = 2; cd = 1; a = {}; Do[If[DefQ[n], If[n - z1 == cd, m = m + 1; If[m > 5, AppendTo[a, n - 5*cd]], m = 2; cd = n - z1]; z1 = n], {n, 3, 1000000}]; a
A228965
Smallest sets of 8 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.
Original entry on oeis.org
221355126, 402640540, 668862580, 739577140
Offset: 1
221355126, 221355128, 221355130, 221355132, 221355134, 221355136, 221355138, 221355140 is the smallest set of 8 consecutive abundant numbers in arithmetic progression so 221355126 is in the list.
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AbundantQ[n_] := DivisorSigma[1, n] > 2 n; m = 2; z1 = 18; cd = 6; a = {}; Do[If[AbundantQ[n], If[n - z1 == cd, m = m + 1; If[m > 7, AppendTo[a, n - 7*cd]], m = 2; cd = n - z1]; z1 = n], {n, 19, 1000000000}]; a
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