1,1

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:

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

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

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

k=3.|...63.|..75..|..99..|.105..|.171..|.195..|.231..|.261..|..273..|..285..|not.yet

k=4.|..297.|.495..|.621..|.693..|.735..|.819..|.855..|.975..|.1029..|.1107..|not.yet

k=5.|.1053.|................................................................|not.yet

k=6.|..729.|................................................................|not.yet

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

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

Adjacent sequences: A140283 A140284 A140285 this_sequence A140287 A140288 A140289

Sequence in context: A132437 A128081 A046635 this_sequence A091713 A111546 A135883

easy,more,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), May 24 2008