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.

2, 4, 6, 8, 12, 30, 16, 24, 60, 210, 32, 48, 120, 420, 2310, 64, 96, 240, 840, 4620, 30030, 128, 192, 480, 1680, 9240, 60060, 510510, 256, 384, 960, 3360, 18480, 120120, 1021020, 9699690, 512, 768, 1920, 6720, 36960, 240240, 2042040, 19399380, 223092870, 1024, 1536, 3840, 13440, 73920, 480480, 4084080, 38798760, 446185740, 6469693230

Offset: 1

Author

Ilya Gutkovskiy, Apr 26 2018

Keywords

• nonn
• tabl

Comments

T(n,k) = the smallest number m having exactly n prime divisors counted with multiplicity and exactly k distinct prime divisors.

Examples

			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).
Triangle begins:
    2;
    4,   6;
    8,  12,  30;
   16,  24,  60,  210;
   32,  48, 120,  420, 2310;
   64,  96, 240,  840, 4620, 30030;
  128, 192, 480, 1680, 9240, 60060, 510510;
  ...
		

Links

• Eric Weisstein's World of Mathematics, Prime Factor
• Eric Weisstein's World of Mathematics, Distinct Prime Factors
• Eric Weisstein's World of Mathematics, Primorial
• Index entries for sequences related to primorial numbers
• Index to sequences related to prime signature

Crossrefs

Cf. A000079, A001221, A001222, A002110, A005179, A038547, A055079, A070175, A303557 (central terms).

Programs

Mathematica

Flatten[Table[2^(n - k) Product[Prime[j], {j, k}], {n, 10}, {k, n}]]