A274607 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.

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, 80, 96, 128, 19, 55, 75, 100, 120, 160, 192, 256, 23, 77, 125, 150, 200, 240, 320, 384, 512, 29, 121, 175, 250, 300, 400, 480, 640, 768, 1024, 31, 143, 275, 375, 500, 600

Offset

1,1

Links

Table of n, a(n) for n=1..61.

Formula

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

T(n,n) = 2^n.

Example

Table starts:
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,  80,  96, 128;
19,  55,  75, 100, 120, 160, 192, 256;
23,  77, 125, 150, 200, 240, 320, 384,  512;
29, 121, 175, 250, 300, 400, 480, 640,  768, 1024;
31, 143, 275, 375, 500, 600, 800, 960, 1280, 1536, 2048;
...
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

Prog

(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)))))

Crossrefs

Cf. A056239.

Sequence in context: A297440 A362134 A232895 * A339607 A262374 A299442

Adjacent sequences: A274604 A274605 A274606 * A274608 A274609 A274610

Keyword

nonn,tabl

Author

David A. Corneth, Jun 30 2016

Status

approved