A079852 a(1) = 1, a(2) = 2, a(3) = 3 and a(n) is the smallest number such that all a(i)*a(j)*a(k) are different.

1, 2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 210, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293, 307, 311, 313, 317, 331

Offset: 1

Author

Amarnath Murthy, Feb 19 2003

Keywords

• nonn

Comments

Note that a(57) = 210 = 2*3*5*7, while 330 = 2*3*5*11 is not in the sequence. This demonstrates that this sequence is not determined by prime signature alone. - Charles R Greathouse IV, Oct 17 2015

Links

• Zak Seidov, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000045, A079850, A066720, A026477.

Programs

Mathematica

f[l_List] := Block[{k = 1,p2 = Times @@@ Subsets[l, {2}], p3 = Times @@@ Subsets[l, {3}]},While[Intersection[p3, p2*k] != {}, k++ ]; Append[l, k]]; Nest[f, {1, 2, 3}, 62] (* Ray Chandler, Feb 12 2007 *)

Extensions

Extended by Ray Chandler, Feb 12 2007

Typo in name fixed by Zak Seidov, Jul 06 2013