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%I #16 May 10 2020 19:30:21
%S 3,15,99,495,2079,4455,36855,70875,280665,1393119,4179357,12931731,
%T 32417901,161026623,514966329,1490692005
%N The n-th lucky number which is the product of exactly n primes (with multiplicity).
%C 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:
%C ============================================================================
%C k | n=1 | n=2 | n=3 | n=4 | n=5 | n=6 | n=7 | n=8 | n=9 | n=10 |in OEIS
%C 1 | 3 | 7 | 13 | 31 | 37 | 43 | 67 | 73 | 79 | 127 |A031157
%C 2 | 9 | 15 | 21 | 25 | 33 | 49 | 51 | 69 | 87 | 93 |A139787
%C 3 | 63 | 75 | 99 | 105 | 171 | 195 | 231 | 261 | 273 | 285 |
%C 4 | 297 | 495 | 621 | 693 | 735 | 819 | 855 | 975 | 1029 | 1107 |
%C 5 | 1053 | |
%C 6 | 729 | |
%C ============================================================================
%C a(16) > 10^9. - _Donovan Johnson_, Oct 24 2010
%e a(4) = 693 because the 113th lucky number = 693 = 3^2 * 7 * 11 is the 4th lucky number with 4 prime factors.
%Y Cf. A000040, A000959, A001358, A014612, A031157, A139787.
%K nonn,more,less
%O 1,1
%A _Jonathan Vos Post_, May 24 2008
%E a(4) corrected and 5 more terms via b000959.txt from _R. J. Mathar_, Oct 22 2010
%E a(10)-a(15) from _Donovan Johnson_, Oct 24 2010
%E a(16) from _Giovanni Resta_, May 10 2020
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