A115758 Triangle where a(1,1)=0. a(n,m) = number of terms among first (n-1) terms of sequence A115759 which are coprime to m. A115759(n) is the sum of terms in the n-th row of triangle A115758.

0, 1, 0, 2, 1, 1, 3, 1, 2, 1, 4, 2, 3, 2, 3, 5, 2, 4, 2, 4, 2, 6, 3, 5, 3, 5, 3, 3, 7, 3, 6, 3, 6, 3, 3, 3, 8, 3, 7, 3, 7, 3, 4, 3, 7, 9, 4, 7, 4, 7, 3, 5, 4, 7, 3, 10, 5, 8, 5, 8, 4, 6, 5, 8, 4, 9, 11, 5, 8, 5, 9, 4, 7, 5, 8, 4, 10, 4, 12, 5, 9, 5, 9, 4, 8, 5, 9, 4, 11, 4, 11, 13, 5, 9, 5, 10, 4, 9, 5, 9, 4

Offset

1,4

Comments

0 is considered here to be coprime only to 1.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150; first 5151 terms from Diana L. Mecum)

Example

The first 4 terms of sequence A115759 are 0, 1, 4 and 7.
Among these there are 4 terms coprime to 1, 2 terms coprime to 2, 3 terms coprime to 3, 2 terms coprime to 4 and 3 terms coprime to 5.
So row 5 of the triangle is [4,2,3,2,3].
(And so A115759(5) = 4+2+3+2+3 = 14.)
From Michael De Vlieger, Sep 29 2017: (Start)
First 12 rows of triangle:
   0
   1  0
   2  1  1
   3  1  2  1
   4  2  3  2  3
   5  2  4  2  4  2
   6  3  5  3  5  3  3
   7  3  6  3  6  3  3  3
   8  3  7  3  7  3  4  3  7
   9  4  7  4  7  3  5  4  7  3
  10  5  8  5  8  4  6  5  8  4   9
  11  5  8  5  9  4  7  5  8  4  10  4
(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]} &, {{{0}}, {0}}, Range[2, 12]] // First // Flatten (* Michael De Vlieger, Sep 29 2017 *)

Crossrefs

Cf. A115756, A115759.

Sequence in context: A175488 A309914 A364911 * A228351 A124734 A337259

Adjacent sequences: A115755 A115756 A115757 * A115759 A115760 A115761

Keyword

nonn,tabl,look

Author

Leroy Quet, Jan 30 2006

Extensions

a(22) and beyond from Diana L. Mecum, Aug 11 2008

Status

approved