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Array, by antidiagonals, A(n,k) = next number that is the product of exactly k primes (not necessarily distinct) after 10*n.
1

%I #28 Oct 28 2021 07:10:34

%S 2,4,11,8,14,23,16,12,21,31,32,16,27,33,41,64,32,24,42,46,53,128,64,

%T 32,36,42,51,61,256,128,64,32,54,52,62,71,512,256,128,64,48,54,63,74,

%U 83,1024,512,256,128,64,72,81,75,82,97,2048,1024,512,256,128,64,72,81,92,91,101,4096,2048,1024,512,256,128,64,72,81,92,106,113,8192,4096,2048,1024,512,256,128,96,108,100,102,111,127

%N Array, by antidiagonals, A(n,k) = next number that is the product of exactly k primes (not necessarily distinct) after 10*n.

%e Table begins:

%e ========================================================

%e ...|n=0|n=1|n=2|n=3|n=4|n=5|n=6|n=7|n=7|n=9|n=10|

%e k=1|.2.|.11|.23|.31|.41|.53|.61|.71|.83|.97|.101|A218255

%e k=2|.4.|.14|.21|.33|.46|.51|.62|.74|.82|.91|.106|A185008

%e k=3|.8.|.12|.27|.42|.42|.52|.63|.75|.92|.92|.102|

%e k=4|16.|.16|.24|.36|.54|.54|.81|.81|.81|100|.104|

%e k=5|32.|.32|.32|.32|.48|.72|.72|.72|108|108|.108|

%e k=6|64.|.64|.64|.64|.64|.64|.64|.96|.96|.96|.144|

%e ========================================================

%p A218643 := proc(n,k)

%p local a;

%p for a from 10*n+1 do

%p if numtheory[bigomega](a) = k then

%p return a;

%p end if;

%p end do:

%p end proc:

%p for d from 1 to 13 do

%p for n from 0 to d-1 do

%p printf("%d,",A218643(n,d-n)) ;

%p end do:

%p end do: # _R. J. Mathar_, Nov 07 2012

%Y Cf. A008592, A218255, A185008.

%K nonn,easy,tabl

%O 1,1

%A _Jonathan Vos Post_, Nov 03 2012