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%I #10 Jul 05 2019 11:43:06
%S 1,1,2,3,10,18,64,72,110,294,315,1296,2000,2100,2530,6084,8526,9450,
%T 33792,38080,46656,53352,82000,106480,248832,270000,275400,322452,
%U 341172,460992,615195,2129920,2515456,2552448,3548448,3596400,4161456
%N a(n) = floor(p/2) * floor(floor(p/2)/2) * floor(floor(floor(p/2)/2)/2) * ... * 1, where p=prime(n).
%C Cumulative product of the residuals of a repeated shift-right operation on the base-2 representation of prime(n).
%H G. C. Greubel, <a href="/A163467/b163467.txt">Table of n, a(n) for n = 1..5000</a>
%e For n=6, p=13, the intermediate factors are floor(13/2)=6, floor(6/2)=3, floor(3/2)=1, which yield a(6)=6*3*1=18.
%e For n=7, p=17, floor(17/2)=8, floor(8/2)=4, floor(4/2)=2, floor(2/2)=1, which yield a(7)=8*4*2*1=64.
%t lst={};Do[p=Prime[n];s=1;While[p>1,p=IntegerPart[p/2];s*=p;];AppendTo[lst,s],{n,5!}];lst
%t Table[Times@@Rest[NestWhileList[Floor[#/2]&,Prime[n],#>1&]],{n,40}] (* _Harvey P. Dale_, Jul 05 2019 *)
%o (PARI) a(n) = my(p=prime(n), k=1); while(p!=1, k *= p\2; p = p\2); k; \\ _Michel Marcus_, Jul 26 2017
%Y Cf. A098844.
%K nonn,easy
%O 1,3
%A _Vladimir Joseph Stephan Orlovsky_, Jul 28 2009
%E More divisions and primes mentioned in the definition by _R. J. Mathar_, Aug 02 2009
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