# array T(k,n) = n-th composite coprime to k, read by antidiagonals

Jonathan Post jvospost3 at gmail.com
Wed Jan 10 20:28:15 CET 2007

```Would anyone want me to turn the below comment (on A126601, as the main
diaginal of the implied array), into a submitted sequence? For example, if I
got the read-out right (would be easier with proportional font, and
alignment with dots):

array T(k,n) = n-th composite coprime to k, read by antidiagonals:
4, 9, 6, 4, 15, 8, 9, 8, 21, 10, 4, 15, 10, 25, 10, ...

Are other rows, columns, and the like already in OEIS besides the ones
I cross-reference below?

COMMENT FROM Jonathan Vos Post RE A126601

%I A126601
%S A126601 4, 15, 10, 25, 12, 77, 15, 39, 26, 69, 20, 121, 22, 81, 56,
69, 27, 161, 30, 121, 65,
%N A126601 a(n) = nth composite from among those composites which are
coprime to n.
%C A126601 *** corrected from erroneous comment of Mon, 8 Jan 2007
13:31:08 -0500 ***
Main diagonal of array T(k,n) = n-th composite coprime to k.
That array begins:
1 | 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ...
2 | 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, ...
3 | 4, 8, 10, 14, 16, 20, 22, 25, 26, 28, 34, ...
4 | 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, ...
5 | 4, 6, 8, 9, 12, 14, 16, 18, 21, 22, 24, 26, ...
6 | 25, 35, 49, 55, 65, 77, 85, 91, 95, 115, 119, ...
7 | 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 22, 24, ...
8 | 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, ...
9 | 4, 8, 10, 14, 16, 20, 22, 25, 26, 28, 34, ...
10| 49, 77, 91, 119, 121, 133, 143, 161, 169, ...
The array has other integer sequences as its various diagonals,
cumulative row sums, cumulative row products, and the like.
Row 1 = A002808 The composite numbers.
Row 2 = A071904 Odd composite numbers.
Row 3 (composites not divisble by 3) not in OEIS?
Row 4 = Row 8 = Row 2.
Row 5 (composites not divisble by 5) not in OEIS?
Row 6 = A038509 Composite numbers with smallest prime factor >= 5.
Row 7 (composites not divisble by 7) not in OEIS?
%Y A126601 Cf. A002808, A038509, A071904.
%O A126601 1
%K A126601 ,easy,nonn,
%A A126601 Jonathan Vos Post (jvospost2 at yahoo.com