A000423 a(n) is smallest number > a(n-1) of form a(i)*a(j), i < j < n.

2, 3, 6, 12, 18, 24, 36, 48, 54, 72, 96, 108, 144, 162, 192, 216, 288, 324, 384, 432, 486, 576, 648, 768, 864, 972, 1152, 1296, 1458, 1536, 1728, 1944, 2304, 2592, 2916, 3072, 3456, 3888, 4374, 4608, 5184, 5832, 6144, 6912, 7776, 8748, 9216, 10368, 11664

Offset: 1

Author

R. Muller

Keywords

• nonn
• easy

Comments

Sequence contains 2, 3 and all numbers of form 2^a*3^b where a >= 1 and b >= 1. - David W. Wilson, Aug 15 1996

Main entry for this sequence is A033845, which is this sequence starting at 6. - Charles R Greathouse IV, Feb 27 2012

References

• Amarnath Murthy, The sum of the reciprocals of the Smarandache multiplicative sequence, (to be published in Smarandache Notions Journal).
• F. Smarandache, "Properties of the Numbers", University of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ
• M. Myers, Smarandache Multiplicative Numbers, in Memorables 1998, Bristol Banner Books, Bristol, p. 37, 1998.

Links

• F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.

Crossrefs

Subsequence of A003586 (3-smooth numbers).

A007335 and A033845 are subsequences.

Programs

Mathematica

a[1] = 2; a[2] = 3; a[n_] := a[n] = For[k = a[n - 1] + 1, True, k++, If[ AnyTrue[Table[a[i] a[j], {i, 1, n-2}, {j, i+1, n-1}] // Flatten, # == k& ], Return[k]]]; Table[an = a[n]; Print[an]; an, {n, 1, 50}] (* Jean-François Alcover, Feb 08 2016 *)

Formula

Sum_{n>=1} 1/a(n) = 4/3. - Amiram Eldar, Jul 31 2022

Extensions

More terms from David W. Wilson, Aug 15 1996