perplexus.info :: Numbers : Triangular Transcension

Triangular Transcension (Posted on 2009-09-22)

Determine the minimum value of a triangular number T such that the total number of positive divisors of T, including 1 and T, exceeds 500.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer solution

| Comment 2 of 3 |

using Mathematica:

Divs[n_]:=Length[Divisors[n]];
Tri[n_]:=n*(n+1)/2;
i=1;
While[Divs[Tri[i]]У500,i++];
Print[i," ",Tri[i]];

gives:
12375 76576500
so the 12,375th Triangle number 76,576,500 is the first to have more than 500 divisors with 576

Posted by Daniel on 2009-09-22 12:12:10

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