A163467 a(n) = floor(p/2) * floor(floor(p/2)/2) * floor(floor(floor(p/2)/2)/2) * ... * 1, where p=prime(n).

1, 1, 2, 3, 10, 18, 64, 72, 110, 294, 315, 1296, 2000, 2100, 2530, 6084, 8526, 9450, 33792, 38080, 46656, 53352, 82000, 106480, 248832, 270000, 275400, 322452, 341172, 460992, 615195, 2129920, 2515456, 2552448, 3548448, 3596400, 4161456

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 28 2009

Keywords

• nonn
• easy

Comments

Cumulative product of the residuals of a repeated shift-right operation on the base-2 representation of prime(n).

Examples

			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.
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.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A098844.

Programs

Mathematica

lst={};Do[p=Prime[n];s=1;While[p>1,p=IntegerPart[p/2];s*=p;];AppendTo[lst,s],{n,5!}];lst
Table[Times@@Rest[NestWhileList[Floor[#/2]&,Prime[n],#>1&]],{n,40}] (* Harvey P. Dale, Jul 05 2019 *)

PARI

a(n) = my(p=prime(n), k=1); while(p!=1, k *= p\2; p = p\2); k; \\ Michel Marcus, Jul 26 2017

Extensions

More divisions and primes mentioned in the definition by R. J. Mathar, Aug 02 2009