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A290600 Irregular triangle T(n, k) read by rows: positive numbers non-coprime to A002808(n) and smaller than A002808(n), sorted increasingly. 3

%I

%S 2,2,3,4,2,4,6,3,6,2,4,5,6,8,2,3,4,6,8,9,10,2,4,6,7,8,10,12,3,5,6,9,

%T 10,12,2,4,6,8,10,12,14,2,3,4,6,8,9,10,12,14,15,16,2,4,5,6,8,10,12,14,

%U 15,16,18,3,6,7,9,12,14,15,18

%N Irregular triangle T(n, k) read by rows: positive numbers non-coprime to A002808(n) and smaller than A002808(n), sorted increasingly.

%C The length of row n is A290599(n).

%C Row n gives the complement of row A038566(A002808(n), k) with respect to [1, 2, ..., A002808(n) - 1].

%F T(n, k) = k-th entry in the list of increasingly sorted numbers of the set {m = 1..A002808(n)-1: gcd(n, m) not equal to 1}.

%e The irregular triangle T(n, k) begins (N(n) = A002808(n)):

%e n N(n) \ k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ...

%e 1 4 2

%e 2 6 2 3 4

%e 3 8 2 4 6

%e 4 9 3 6

%e 5 10 2 4 5 6 8

%e 6 12 2 3 4 6 8 9 10

%e 7 14 2 4 6 7 8 10 12

%e 8 15 3 5 6 9 10 12

%e 9 16 2 4 6 8 10 12 14

%e 10 18 2 3 4 6 8 9 10 12 14 15 16

%e 11 20 2 4 5 6 8 10 12 14 15 16 18

%e 12 21 3 6 7 9 12 14 15 18

%e 13 22 2 4 6 8 10 11 12 14 16 18 20

%e 14 24 2 3 4 6 8 9 10 12 14 15 16 18 20 21 22

%e 15 25 5 10 15 20

%e ...

%t Table[With[{c = FixedPoint[n + PrimePi@ #] + 1 &, n + PrimePi@ n + 1]}, Select[Range[c - 1], ! CoprimeQ[#, c] &]], {n, 12}] // Flatten (* _Michael De Vlieger_, Sep 03 2017 *)

%Y Cf. A002808, A038566, A290599, A290601, A290602.

%K nonn,tabf

%O 1,1

%A _Wolfdieter Lang_, Aug 30 2017

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Last modified August 20 04:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)