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%I #7 Apr 26 2018 17:43:53
%S 2,4,6,8,12,30,16,24,60,210,32,48,120,420,2310,64,96,240,840,4620,
%T 30030,128,192,480,1680,9240,60060,510510,256,384,960,3360,18480,
%U 120120,1021020,9699690,512,768,1920,6720,36960,240240,2042040,19399380,223092870,1024,1536,3840,13440,73920,480480,4084080,38798760,446185740,6469693230
%N Triangle read by rows: T(n,k) = 2^(n-k)*prime(k)#, 1 <= k <= n, where prime(k)# is the product of first k primes.
%C T(n,k) = the smallest number m having exactly n prime divisors counted with multiplicity and exactly k distinct prime divisors.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Primorial.html">Primorial</a>
%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%e T(5,4) = 420 = 2^2*3*5*7, hence 420 is the smallest number m such that bigomega(m) = 5 and omega(m) = 4 (see A189982).
%e Triangle begins:
%e 2;
%e 4, 6;
%e 8, 12, 30;
%e 16, 24, 60, 210;
%e 32, 48, 120, 420, 2310;
%e 64, 96, 240, 840, 4620, 30030;
%e 128, 192, 480, 1680, 9240, 60060, 510510;
%e ...
%t Flatten[Table[2^(n - k) Product[Prime[j], {j, k}], {n, 10}, {k, n}]]
%Y Cf. A000079, A001221, A001222, A002110, A005179, A038547, A055079, A070175, A303557 (central terms).
%K nonn,tabl
%O 1,1
%A _Ilya Gutkovskiy_, Apr 26 2018
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