A140286 The n-th lucky number which is the product of exactly n primes (with multiplicity).

3, 15, 99, 495, 2079, 4455, 36855, 70875, 280665, 1393119, 4179357, 12931731, 32417901, 161026623, 514966329, 1490692005

Offset: 1

Author

Jonathan Vos Post, May 24 2008

Keywords

• nonn
• more
• less

Comments

This is the main diagonal of the infinite array A(k,n) = n-th n-th lucky number to be the product of exactly k primes, with multiplicity, which begins as below:

============================================================================

k | n=1 | n=2 | n=3 | n=4 | n=5 | n=6 | n=7 | n=8 | n=9 | n=10 |in OEIS

1 | 3 | 7 | 13 | 31 | 37 | 43 | 67 | 73 | 79 | 127 |A031157

2 | 9 | 15 | 21 | 25 | 33 | 49 | 51 | 69 | 87 | 93 |A139787

3 | 63 | 75 | 99 | 105 | 171 | 195 | 231 | 261 | 273 | 285 |

4 | 297 | 495 | 621 | 693 | 735 | 819 | 855 | 975 | 1029 | 1107 |

5 | 1053 | |

6 | 729 | |

============================================================================

a(16) > 10^9. - Donovan Johnson, Oct 24 2010

Examples

			a(4) = 693 because the 113th lucky number = 693 = 3^2 * 7 * 11 is the 4th lucky number with 4 prime factors.
		

Crossrefs

Cf. A000040, A000959, A001358, A014612, A031157, A139787.

Extensions

a(4) corrected and 5 more terms via b000959.txt from R. J. Mathar, Oct 22 2010

a(10)-a(15) from Donovan Johnson, Oct 24 2010

a(16) from Giovanni Resta, May 10 2020