

A126260


Irregular triangle read by rows where row n contains the positive integers k, k<=n, where every positive integer <=k and coprime to k is also coprime to n.


6



1, 1, 2, 1, 2, 3, 1, 2, 4, 1, 2, 3, 4, 5, 1, 2, 6, 1, 2, 3, 4, 5, 6, 7, 1, 2, 4, 6, 8, 1, 2, 3, 6, 9, 1, 2, 4, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 2, 6, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 4, 6, 14, 1, 2, 3, 15, 1, 2, 4, 6, 8, 10, 12, 14, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
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OFFSET

1,3


COMMENTS

The first term of each row is 1. The second term of each row, except for row 1, is 2. The last term of row n is n.


LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..12325 (rows 1 <= n <= 300).


EXAMPLE

Table begins:
1
1,2
1,2,3
1,2,4
1,2,3,4,5
1,2,6
...
Row 10 is (1,2,4,10) because the positive integers <=1 and coprime to 1 are {1}, for 2 they are {1}, for 4 they are {1,3}, for 10 they are {1,3,7, 9}; and 1,1,1,3,1,3,7,9 are each coprime to 10.


MATHEMATICA

f[n_] := Select[Range[n], GCD[ #, n] == 1 &]; g[n_] := Select[Range[n], Times @@ GCD[f[ # ], n] == 1 &]; Flatten@Table[g[n], {n, 17}] (* Ray Chandler, Dec 24 2006 *)
Table[Select[Range@ n, Function[k, AllTrue[Select[Range@ k, CoprimeQ[#, k] &], CoprimeQ[#, n] &]]], {n, 17}] // Flatten (* Michael De Vlieger, Aug 21 2017 *)


CROSSREFS

Sequence in context: A136311 A243884 A334428 * A264846 A265691 A214614
Adjacent sequences: A126257 A126258 A126259 * A126261 A126262 A126263


KEYWORD

nonn,tabf


AUTHOR

Leroy Quet, Dec 22 2006


EXTENSIONS

Extended by Ray Chandler, Dec 24 2006


STATUS

approved



