Early 1914 Ramanujan arrived in England. During the mornings he worked with Hardy and in the afternoons he followed lectures. One of the topics he was working on when he came to England were what Ramanujan called "highly composite numbers".

A highly composite number is a positive integer with more divisors than any positive integer smaller than itself.

The earliest paper of Ramanujan I could find was communicated by Hardy and published in the Proceedings of the London Mathematical Society; January 1915, Vol. 14 Issue: 1 p347-347, 1p.

If you have access this is a link: Highly Composite Numbers. ( pdf - 63 pages ).

page 2 of the paper |

Update: 31/3-'11

The paper on highly composite numbers was not the first paper of Ramanujan. He published before he came to England in the Indian Journal of Mathematics. According to the "collected papers of Ramanujan", it was his 15th publication.

So 12 would be highly composite then?

ReplyDeleteYep. The highly composites are...

ReplyDeleten d(n)

1 1

2 2

4 3

6 4

12 6

24 8

etc.