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

1,1

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

Table of n, a(n) for n=1..49.

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

Formula

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

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 *)

Crossrefs

Subsequence of A003586 (3-smooth numbers).

A007335 and A033845 are subsequences.

Sequence in context: A280681 A328899 A093687 * A007335 A309311 A361693

Adjacent sequences: A000420 A000421 A000422 * A000424 A000425 A000426

Keyword

nonn,easy

Author

R. Muller

Extensions

More terms from David W. Wilson, Aug 15 1996

Status

approved