A076034 Group the natural numbers so that the n-th group contains the smallest set of n relatively prime numbers: (1), (2, 3), (4, 5, 7), (6, 11, 13, 17), (8, 9, 19, 23, 25), (10, 21, 29, 31, 37, 41), ...

1, 2, 3, 4, 5, 7, 6, 11, 13, 17, 8, 9, 19, 23, 25, 10, 21, 29, 31, 37, 41, 12, 35, 43, 47, 53, 59, 61, 14, 15, 67, 71, 73, 79, 83, 89, 16, 27, 49, 55, 97, 101, 103, 107, 109, 18, 65, 77, 113, 127, 131, 137, 139, 149, 151, 20, 33, 91, 157, 163, 167, 173, 179, 181, 191, 193

Offset: 1

Author

Amarnath Murthy, Oct 01 2002

Keywords

• nonn
• tabl
• look

Examples

			The triangle begins:
   1;
   2, 3;
   4,  5,  7;
   6, 11, 13, 17;
   8,  9, 19, 23, 25;
  10, 21, 29, 31, 37, 41;
  ...
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Paul Tek, PERL program for this sequence

Crossrefs

Cf. A075383, A076032, A076033, A095167.

Programs

Maple

S:=[$1..1000]: Res:= NULL:
for n from 1 to 20 do
  A:= [S[1]]; R:= 1; count:= 1;
  for k from 2 while count < n do
    if andmap(t -> igcd(t,S[k])=1, A) then count:= count+1; A:= [op(A),S[k]]; R:= R,k; fi
  od;
  S:= subsop(op(map(t -> t=NULL, [R])),S);
  Res:= Res, op(A);
od:
Res; # Robert Israel, Dec 04 2022

Perl

# See Links section.

Extensions

More terms from David Wasserman, Jan 29 2005

Crossrefs added by Paul Tek, Oct 24 2015