[seqfan] A subsequence of highly composite numbers A002182 ?

peter.luschny at googlemail.com peter.luschny at googlemail.com
Sat Jun 20 17:39:00 CEST 2009

A subsequence of highly composite numbers A002182?

While contemplating some totally different matter
I observed a cute little formula producing only highly
composite numbers. After deleting the duplicate
values the resulting sequence starts


In Maple parlance the formula is

rho := proc(n) local m,k; m := nops(convert(n,base,2));
mul(iquo(n,2^k)!/iquo(n,2^(k+1))!^2,k=1..m-1) end:

The sequence is then given by

seq(rho(i),i=1..50): A:=sort(convert({%},list));

Can anyone prove that the formula produces only
highly composite numbers?

Cheers Peter

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