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

1,1

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

Links

Table of n, a(n) for n=1..16.

Example

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.

Sequence in context: A128081 A370676 A186264 * A199416 A046635 A208426

Adjacent sequences: A140283 A140284 A140285 * A140287 A140288 A140289

Keyword

nonn,more,less

Author

Jonathan Vos Post, May 24 2008

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

Status

approved