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

1,1

Comments

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

Links

Table of n, a(n) for n=1..55.

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

Example

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;
  ...

Mathematica

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

Crossrefs

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

Sequence in context: A059901 A036035 A063008 * A136101 A187779 A086141

Adjacent sequences: A303552 A303553 A303554 * A303556 A303557 A303558

Keyword

nonn,tabl

Author

Ilya Gutkovskiy, Apr 26 2018

Status

approved