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A303555 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.

%I A303555 #8 Feb 16 2025 08:33:54
%S A303555 2,4,6,8,12,30,16,24,60,210,32,48,120,420,2310,64,96,240,840,4620,
%T A303555 30030,128,192,480,1680,9240,60060,510510,256,384,960,3360,18480,
%U A303555 120120,1021020,9699690,512,768,1920,6720,36960,240240,2042040,19399380,223092870,1024,1536,3840,13440,73920,480480,4084080,38798760,446185740,6469693230
%N A303555 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 A303555 T(n,k) = the smallest number m having exactly n prime divisors counted with multiplicity and exactly k distinct prime divisors.
%H A303555 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>
%H A303555 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%H A303555 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Primorial.html">Primorial</a>
%H A303555 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%H A303555 <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%e A303555 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 A303555 Triangle begins:
%e A303555     2;
%e A303555     4,   6;
%e A303555     8,  12,  30;
%e A303555    16,  24,  60,  210;
%e A303555    32,  48, 120,  420, 2310;
%e A303555    64,  96, 240,  840, 4620, 30030;
%e A303555   128, 192, 480, 1680, 9240, 60060, 510510;
%e A303555   ...
%t A303555 Flatten[Table[2^(n - k) Product[Prime[j], {j, k}], {n, 10}, {k, n}]]
%Y A303555 Cf. A000079, A001221, A001222, A002110, A005179, A038547, A055079, A070175, A303557 (central terms).
%K A303555 nonn,tabl
%O A303555 1,1
%A A303555 _Ilya Gutkovskiy_, Apr 26 2018