[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?
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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
1,2,6,12,60,120,840,7560,15120,110880,166320,1441440,
2882880,10810800,43243200,183783600,367567200,
2793510720,6983776800,58663725120,117327450240,
299836817280,2698531355520,7495920432000,...
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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