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

1,3

Comments

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A098844.

Sequence in context: A298345 A057507 A233895 * A143045 A156909 A215121

Adjacent sequences: A163464 A163465 A163466 * A163468 A163469 A163470

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 28 2009

Extensions

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

Status

approved