A115756 Triangle where a(1,1)=1. a(n,m) = number of terms among first (n-1) terms of sequence A115757 which are coprime to m. A115757(n) is the sum of terms in the n-th row of triangle A115756.

1, 1, 1, 2, 1, 2, 3, 2, 3, 2, 4, 2, 4, 2, 2, 5, 2, 5, 2, 3, 2, 6, 3, 6, 3, 4, 3, 5, 7, 3, 6, 3, 4, 3, 6, 3, 8, 4, 7, 4, 4, 4, 6, 4, 7, 9, 4, 7, 4, 5, 4, 7, 4, 7, 2, 10, 5, 8, 5, 6, 5, 8, 5, 8, 3, 10, 11, 6, 9, 6, 7, 6, 9, 6, 9, 4, 11, 6, 12, 6, 9, 6, 7, 6, 10, 6, 9, 4, 12, 6, 12, 13, 7, 9, 7, 7, 6

Offset

1,4

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150, first 2850 terms / 75 rows from Diana L. Mecum)

Example

The first 4 terms of sequence A115757 are 1, 2, 5 and 10.
Among these there are 4 terms coprime to 1, 2 terms coprime to 2, 4 terms coprime to 3, 2 terms coprime to 4 and 2 terms coprime to 5.
So row 5 of the triangle is [4,2,4,2,2].
(And so A115757(5) = 4+2+4+2+2 = 14.)
From Michael De Vlieger, Sep 29 2017: (Start)
First 12 rows of triangle:
   1
   1  1
   2  1  2
   3  2  3  2
   4  2  4  2  2
   5  2  5  2  3  2
   6  3  6  3  4  3  5
   7  3  6  3  4  3  6  3
   8  4  7  4  4  4  6  4  7
   9  4  7  4  5  4  7  4  7  2
  10  5  8  5  6  5  8  5  8  3  10
  11  6  9  6  7  6  9  6  9  4  11  6
(End)

Mathematica

Fold[{Append[#1, #3], Append[#2, Total@ #3]} & @@ {First@ #1, Last@ #1, Map[Function[m, Count[Last@ #1, k_ /; CoprimeQ[m, k]]], Range@ #2]} &, {{{1}}, {1}}, Range[2, 12]] // First // Flatten (* Michael De Vlieger, Sep 29 2017 *)

Crossrefs

Cf. A115757, A115758.

Sequence in context: A268835 A006641 A191408 * A067731 A147844 A291985

Adjacent sequences: A115753 A115754 A115755 * A115757 A115758 A115759

Keyword

nonn,tabl

Author

Leroy Quet, Jan 30 2006

Extensions

Terms 22 through 2850 from Diana L. Mecum, Aug 09 2008

Status

approved