This title space is too small! The topic is Hardy-Ramanujan numbers. #4

Computer Science Level 3

This problem's question: 87539319 is first sum of paired cubes that can be done three different ways. What is the sum of the positive integers that comprise those three pairs (six positive integers altogether)?

See A011541 .

This is not a pencil-and-paper problem. It does take a small number of milliseconds on a 4.5GHz computer to find the pairs, which are not in the link mentioned above.

The answer is 1923.

1 solution

A Former Brilliant Member
Jun 16, 2019

The upper limit on the positive integers to be checked: $445$

The three pairs, which when cubed sum to 87539319 :

$\begin{array}{cc} 167 & 436 \\ 228 & 423 \\ 255 & 414 \\ \end{array}$

The sum of the positive integers that comprise the pairs: $1923$

s = 87539319;
q = Timing[n = Ceiling[N[Power[s, (3)^-1]]];
   Print[n];
   c = Table[i^3, {i, n}];
   ParallelTable[j = Power[s - i^3, (3)^-1]; 
    If[j \[Element] Integers \[And] i <= j, {i, j}, Nothing], {i, n}]
   ];
Print[q];
Print[Plus @@ Flatten[q[[2]]]]

This title space is too small! The topic is Hardy-Ramanujan numbers. #4

The answer is 1923.

1 solution

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