A362813 Number of numbers that occur more than once in column n of McGarvey's array (A007062).
0, 2, 3, 4, 6, 6, 7, 9, 11, 12, 14, 13, 14, 16, 15, 17, 21, 20, 22, 25, 24, 25, 29, 26, 26, 31, 29, 31, 36, 33, 33, 40, 37, 36, 44, 41, 39, 48, 42, 44, 50, 44, 48, 53, 49, 49, 56, 54, 53, 62, 55, 56, 69, 61, 59, 66, 61, 66, 73, 65, 64, 75, 71, 70, 80, 72, 71
Offset: 1
Keywords
Examples
Corner of McGarvey's array (from A007062): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 4 1 2 5 6 3 10 7 8 11 12 9 16 13 14 17 18 15 22 19 5 2 1 4 7 10 3 6 9 12 11 8 17 14 13 16 19 22 15 18 7 4 1 2 5 12 8 6 3 10 13 14 17 8 11 18 15 22 19 16 12 5 2 1 4 7 14 13 10 3 6 8 22 15 18 11 8 17 24 23 14 7 4 1 2 5 12 15 22 8 6 3 10 13 20 23 24 17 8 11 15 12 5 2 1 4 7 14 23 20 13 10 3 6 8 22 25 28 31 18 (Column 3) = (3,4,2,1,1,2,4,5,7,12,23,...) in which the numbers 1,2,4 occur more than once.
Programs
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Mathematica
a = Range[x = 40000]; rows = Table[a = Flatten[Map[Reverse, Partition[a, n]]], {n, NestWhile[# + 1 &, 1, (x = # Floor[x/#]) > 0 &] - 1}]; Flatten[Table[{Length[Select[SortBy[Tally[Map[#[[col]] &, rows]], #[[2]] &], #[[2]] > 1 &]]}, {col, 100}]] (* Peter J. C. Moses, May 01 2023 *)