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

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

Offset

1,1

Comments

The length of row n is A290599(n).

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

Links

Table of n, a(n) for n=1..71.

Formula

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}.

Example

The irregular triangle T(n, k) begins (N(n) = A002808(n)):
n   N(n) \ k  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 ...
1   4         2
2   6         2  3  4
3   8         2  4  6
4   9         3  6
5   10        2  4  5  6  8
6   12        2  3  4  6  8  9 10
7   14        2  4  6  7  8 10 12
8   15        3  5  6  9 10 12
9   16        2  4  6  8 10 12 14
10  18        2  3  4  6  8  9 10 12 14 15 16
11  20        2  4  5  6  8 10 12 14 15 16 18
12  21        3  6  7  9 12 14 15 18
13  22        2  4  6  8 10 11 12 14 16 18 20
14  24        2  3  4  6  8  9 10 12 14 15 16 18 20 21 22
15  25        5 10 15 20
...

Mathematica

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 *)

Crossrefs

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

Sequence in context: A238958 A238971 A194331 * A143595 A211702 A208521

Adjacent sequences: A290597 A290598 A290599 * A290601 A290602 A290603

Keyword

nonn,tabf

Author

Wolfdieter Lang, Aug 30 2017

Status

approved