cp's OEIS Frontend

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

%I A290600 #16 Jun 17 2025 05:20:44
%S A290600 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 A290600 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 A290600 15,16,18,3,6,7,9,12,14,15,18
%N A290600 Irregular triangle T(n, k) read by rows: positive numbers non-coprime to A002808(n) and smaller than A002808(n), sorted increasingly.
%C A290600 The length of row n is A290599(n).
%C A290600 Row n gives the complement of row A038566(A002808(n), k) with respect to [1, 2, ..., A002808(n) - 1].
%F A290600 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 A290600 The irregular triangle T(n, k) begins (N(n) = A002808(n)):
%e A290600   n   N(n) \ k  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 ...
%e A290600   1   4         2
%e A290600   2   6         2  3  4
%e A290600   3   8         2  4  6
%e A290600   4   9         3  6
%e A290600   5   10        2  4  5  6  8
%e A290600   6   12        2  3  4  6  8  9 10
%e A290600   7   14        2  4  6  7  8 10 12
%e A290600   8   15        3  5  6  9 10 12
%e A290600   9   16        2  4  6  8 10 12 14
%e A290600   10  18        2  3  4  6  8  9 10 12 14 15 16
%e A290600   11  20        2  4  5  6  8 10 12 14 15 16 18
%e A290600   12  21        3  6  7  9 12 14 15 18
%e A290600   13  22        2  4  6  8 10 11 12 14 16 18 20
%e A290600   14  24        2  3  4  6  8  9 10 12 14 15 16 18 20 21 22
%e A290600   15  25        5 10 15 20
%e A290600   ...
%t A290600 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 A290600 Cf. A002808, A038566, A290599, A290601, A290602.
%K A290600 nonn,tabf
%O A290600 1,1
%A A290600 _Wolfdieter Lang_, Aug 30 2017