A131504 Array read by antidiagonals: a(m,n) = m-th integer from among those positive integers that are coprime to (m*n).

1, 1, 3, 1, 3, 4, 1, 5, 7, 7, 1, 3, 4, 7, 6, 1, 3, 7, 11, 11, 17, 1, 5, 4, 7, 8, 17, 8, 1, 3, 7, 9, 11, 17, 15, 15, 1, 3, 4, 11, 6, 17, 11, 15, 13, 1, 5, 7, 9, 17, 19, 15, 23, 25, 23, 1, 3, 4, 7, 6, 17, 9, 15, 13, 23, 12, 1, 3, 11, 11, 11, 19, 23, 19, 25, 37, 23, 35, 1, 5, 4, 9, 8, 17, 8, 23, 16

Offset: 1

Author

Leroy Quet, Aug 13 2007

Keywords

• nonn
• tabl

Examples

			For example:
a(6,5) = 19 because the positive integers which are coprime to (5*6) are 1,7,11,13,17,19,23,29,... and the 6th of these is 19.
Array begins:
1, 3, 4, 7, 6,17, 8,15,13,23,12,35,14,...
1, 3, 7, 7,11,17,15,15,25,23,23,35,27,...
1, 5, 4,11, 8,17,11,23,13,37,17,35,20,...
1, 3, 7, 7,11,17,15,15,25,23,23,35,27,...
1, 3, 4, 9, 6,19, 9,19,16,23,14,43,17,...
1, 5, 7,11,17,17,23,23,25,37,35,35,41,...
1, 3, 4, 9, 6,19, 8,17,16,29,13,41,16,...
1, 3, 7, 7,11,17,15,15,25,23,23,35,27,...
1, 5, 4,11, 8,17,11,23,13,37,17,35,20,...
1, 3,11, 9,11,19,19,19,31,23,29,43,33,...
1, 3, 4, 7, 6,19, 8,17,14,27,12,37,15,...
1, 5, 7,11,17,17,23,23,25,37,35,35,41,...
		

Crossrefs

Cf. A069213.

Programs

Maple

A131504 := proc(n,m) local mn,a,k ; mn := m*n ; k := 1; for a from 1 do if gcd(a,mn) = 1 then if k = m then RETURN(a) ; fi ; k := k+1 ; fi ; od: end: for d from 1 to 14 do for m from 1 to d do printf("%d,",A131504(d+1-m,m)) ; od: od: # R. J. Mathar, Oct 26 2007

Extensions

More terms from R. J. Mathar, Oct 26 2007