(49g 50g) Eta Quotients

[John Keith]

The following program computes sequences known as "multiplicative eta quotients". While this might sound obscure, they include several well-known sequences including the partition numbers and the Ramanujan tau sequence. In fact, this is an efficient program for computing the tau sequence, and is a generalization of the third program in post #1 of this thread.

The program requires the SUMDIVISORS program and the ListExt Library.

A full explanation can be found in this paper, and a complete list of sequences here.

Code:


\<< SWAP NEG \-> n m
  \<< n LSEQ 1 SUMDIVISORS { 1 } 1 n
    FOR k OVER 1 k SUB OVER REV * LSUM m * k / +
    NEXT NIP
  \>>
\>>

To use the program, level 2 should have an integer representing the denominator of the quotient. Level 1 should have an integer representing the number of terms that the program will return. For example, with 24 on level 2 and 50 on level 1, the program will return the first 50 Ramanujan tau numbers.