A320436 Irregular triangle read by rows where T(n,k) is the number of pairwise coprime k-subsets of {1,...,n}, 1 <= k <= A036234(n), where a single number is not considered to be pairwise coprime unless it is equal to 1.

1, 1, 1, 1, 3, 1, 1, 5, 2, 1, 9, 7, 2, 1, 11, 8, 2, 1, 17, 19, 10, 2, 1, 21, 25, 14, 3, 1, 27, 37, 24, 6, 1, 31, 42, 26, 6, 1, 41, 73, 68, 32, 6, 1, 45, 79, 72, 33, 6, 1, 57, 124, 151, 105, 39, 6, 1, 63, 138, 167, 114, 41, 6, 1, 71, 159, 192, 128, 44, 6, 1, 79

Offset

1,5

Links

Table of n, a(n) for n=1..72.

Example

Triangle begins:
   1
   1   1
   1   3   1
   1   5   2
   1   9   7   2
   1  11   8   2
   1  17  19  10   2
   1  21  25  14   3
   1  27  37  24   6
   1  31  42  26   6
   1  41  73  68  32   6
   1  45  79  72  33   6
   1  57 124 151 105  39   6
   1  63 138 167 114  41   6
   1  71 159 192 128  44   6
   1  79 183 228 157  56   8

Mathematica

Table[Length[Select[Subsets[Range[n], {k}], CoprimeQ@@#&]], {n, 16}, {k, PrimePi[n]+1}]

Crossrefs

Except for the k = 1 column, same as A186974.

Row sums are A320426.

Second column is A015614.

Cf. A051424, A084422, A085945, A187106, A276187, A320423, A320430, A320435.

Sequence in context: A348641 A014475 A358612 * A135228 A021325 A174609

Adjacent sequences: A320433 A320434 A320435 * A320437 A320438 A320439

Keyword

nonn,tabf

Author

Gus Wiseman, Jan 08 2019

Status

approved