From the Odd Division Table to Prime-Power Towers

Abstract. From the odd division table to prime-power towers. The remainder field R(H,j) = 2(H-j+1) mod (2j+1) makes every column one arithmetic progression; the resulting factor map is identified as Sundaram's sieve (1934), the preimage multiplicity is tau(n)-2, and the table reduces to intersections of prime-power layers. The compression over trial division is a factor of about 3, asymptotically only (log N)/2 - the prime number theorem, and nothing better.