A114718 -id:A114718

Search: a114718 -id:a114718

Displaying 1-2 of 2 results found.

page 1

A112599

Triangle where a(1,1) = 1, a(n,m) = number of terms of row (n-1) which are coprime to m.

+10
5

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

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

OFFSET

1,4

COMMENTS

GCD(m,0) is considered here to be m, so 0 is coprime to no positive integer but 1.

LINKS

Ivan Neretin, Rows n = 1..101, flattened

EXAMPLE

Row 6 of the triangle is [5,0,4,0,4,0]. Among these terms there are 6 terms coprime to 1, 1 term coprime to 2, 3 terms coprime to 3, 1 term coprime to 4, 2 terms coprime to 5, 1 term coprime to 6 and 3 terms coprime to 7. So row 7 is [6,1,3,1,2,1,3].

1 1

2 2 2

3 0 3 0

4 2 0 2 2

5 0 4 0 4 0

6 1 3 1 2 1 3

7 5 4 5 7 3 7 5

8 7 7 7 5 6 5 7 7

9 7 8 7 7 7 4 7 8 5

MATHEMATICA

f[l_] := Block[{p, t}, p = l[[ -1]]; k = Length[p]; t = Table[ Sum[ If[GCD[p[[j]], n] == 1, 1, 0], {j, k}], {n, k + 1}]; Return[Append[l, t]]; ]; Flatten[Nest[f, {{1}}, 13]] (* Ray Chandler, Dec 24 2005 *)

CROSSREFS

Row sums are in A114718. - Klaus Brockhaus, Jun 01 2009

KEYWORD

nonn,tabl,look

AUTHOR

Leroy Quet, Dec 21 2005

EXTENSIONS

Extended by Ray Chandler, Dec 24 2005

STATUS

approved

A114719

a(n) = sum of terms in n-th row of triangle A112592.

+10
2

0, 1, 4, 10, 14, 15, 21, 34, 40, 50, 74, 62, 78, 81, 140, 170, 153, 161, 277, 227, 313, 260, 332, 304, 406, 334, 383, 504, 614, 632, 643, 539, 775, 764, 775, 664, 1003, 974, 1095, 847, 917, 1144, 1230, 1140, 1309, 1203, 1413, 1265, 1438, 1698, 1510, 1035, 1194

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

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

The 7th row of triangle A112592 is [6,3,3,3,0,3,3]. So a(7) = 6+3+3+3+0+3+3 = 21.

MATHEMATICA

f[l_] := Block[{p, t}, p = l[[ -1]]; k = Length @ p; t = Table[Count[GCD[p, n], 1], {n, k + 1}]; Return @ Append[l, t]; ]; Plus @@@ Nest[f, {{0}}, 52] (* Robert G. Wilson v *)

CROSSREFS

Cf. A112592, A114718.

KEYWORD

nonn

AUTHOR

Leroy Quet, Dec 27 2005

EXTENSIONS

More terms from Robert G. Wilson v, Dec 28 2005

Typos in Mma program corrected by Giovanni Resta, Jun 12 2016

STATUS

approved

page 1

Search completed in 0.006 seconds