%I #15 Sep 29 2017 11:50:06

%S 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,

%T 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,

%U 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

%N 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.

%H Michael De Vlieger, <a href="/A115756/b115756.txt">Table of n, a(n) for n = 1..11325</a> (rows 1 <= n <= 150, first 2850 terms / 75 rows from Diana L. Mecum)

%e The first 4 terms of sequence A115757 are 1, 2, 5 and 10.

%e 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.

%e So row 5 of the triangle is [4,2,4,2,2].

%e (And so A115757(5) = 4+2+4+2+2 = 14.)

%e From _Michael De Vlieger_, Sep 29 2017: (Start)

%e First 12 rows of triangle:

%e 1

%e 1 1

%e 2 1 2

%e 3 2 3 2

%e 4 2 4 2 2

%e 5 2 5 2 3 2

%e 6 3 6 3 4 3 5

%e 7 3 6 3 4 3 6 3

%e 8 4 7 4 4 4 6 4 7

%e 9 4 7 4 5 4 7 4 7 2

%e 10 5 8 5 6 5 8 5 8 3 10

%e 11 6 9 6 7 6 9 6 9 4 11 6

%e (End)

%t 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 *)

%Y Cf. A115757, A115758.

%K nonn,tabl

%O 1,4

%A _Leroy Quet_, Jan 30 2006

%E Terms 22 through 2850 from _Diana L. Mecum_, Aug 09 2008