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Triangle read by rows: T(n, k) is the largest number that can be formed by multiplying k primes prime(i1),...,prime(ik) such that i1+...+ik = n.
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%I #22 Aug 24 2016 15:29:50

%S 2,3,4,5,6,8,7,10,12,16,11,15,20,24,32,13,25,30,40,48,64,17,35,50,60,

%T 80,96,128,19,55,75,100,120,160,192,256,23,77,125,150,200,240,320,384,

%U 512,29,121,175,250,300,400,480,640,768,1024,31,143,275,375,500,600

%N Triangle read by rows: T(n, k) is the largest number that can be formed by multiplying k primes prime(i1),...,prime(ik) such that i1+...+ik = n.

%F T(n,1) = prime(n).

%F T(n,n) = 2^n.

%e Table starts:

%e 2;

%e 3, 4;

%e 5, 6, 8;

%e 7, 10, 12, 16;

%e 11, 15, 20, 24, 32;

%e 13, 25, 30, 40, 48, 64;

%e 17, 35, 50, 60, 80, 96, 128;

%e 19, 55, 75, 100, 120, 160, 192, 256;

%e 23, 77, 125, 150, 200, 240, 320, 384, 512;

%e 29, 121, 175, 250, 300, 400, 480, 640, 768, 1024;

%e 31, 143, 275, 375, 500, 600, 800, 960, 1280, 1536, 2048;

%e ...

%e The ways of representing 6 as a sum of 3 positive integers are 6 = 1 + 1 + 4, 6 = 1 + 2 + 3, and 6 = 2 + 2 + 2. Since prime(1)*prime(2)*prime(3) = 2*3*5 = 30 is greater than both prime(1)*prime(1)*prime(4) = 2*2*7 = 28 and prime(2)*prime(2)*prime(2) = 3*3*3 = 27, T(6,3) = 30. - _Michael B. Porter_, Jul 28 2016

%o (PARI) T(n, k) = if(k>n,1,if(k==1,prime(n),vecmax(vector(n-1,i,T(n-i,k-1) * prime(i)))))

%Y Cf. A056239.

%K nonn,tabl

%O 1,1

%A _David A. Corneth_, Jun 30 2016