Hardy Diagonals

Hardy's reasons for constructing H(m,2) are beyond our scope. We only exhibit his simple algorithm. In the table below, each row is created from the row above by an obvious sieve process. The diagonal is then read.

Hardy Table

1																									3																									5																									7																									9																									11																									13																									15																									17
1																									5																									9																									13																									17																									21																									25																									29																									33
1																									9																									17																									25																									33																									41																									49																									57																									65
1																									17																									33																									49																									65																									81																									97																									113																									129
1																									33																									65																									97																									129																									161																									193																									225																									257
1																									65																									129																									193																									257																									321																									385																									449																									513

Hardy repeats this process recursively, but his higher order sequences do not seem to have reappeared in the literature.