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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.
3
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
Sequence in context: A268835 A006641 A191408 * A067731 A147844 A291985
KEYWORD
nonn,tabl
AUTHOR
Leroy Quet, Jan 30 2006
EXTENSIONS
Terms 22 through 2850 from Diana L. Mecum, Aug 09 2008
STATUS
approved