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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 12 06:46 EDT 2020. Contains 335658 sequences. (Running on oeis4.)