A300951 a(n) = Product_{j=1..floor(n/2)} p(j) where p(j) = j if j is prime else 1.

1, 1, 1, 1, 2, 2, 6, 6, 6, 6, 30, 30, 30, 30, 210, 210, 210, 210, 210, 210, 210, 210, 2310, 2310, 2310, 2310, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 510510, 510510, 510510, 510510, 9699690, 9699690, 9699690, 9699690, 9699690, 9699690, 9699690

Offset

0,5

Comments

a(4*n+2)=a(4*n+3)=a(4*n+4)=a(4*n+5) for n >= 1. - Robert Israel, Mar 16 2018

The length of the n-th run is given by 2*A054541(n). - Michel Marcus, Mar 17 2018

Links

Robert Israel, Table of n, a(n) for n = 0..4713

Formula

a(n) = A002110(A056172(n)). - Robert Israel, Mar 16 2018

Maple

a := n -> mul(`if`(isprime(j), j, 1), j=1..iquo(n, 2)):
seq(a(n), n=0..44);
# Alternative:
f:= proc(n) option remember;
  if n::even and isprime(n/2) then procname(n-1)*n/2 else procname(n-1) fi
end proc:
f(0):= 1:
map(f, [$0..100]); # Robert Israel, Mar 16 2018

Mathematica

{#, #}&/@FoldList[Times, Table[If[PrimeQ[n], n, 1], {n, 0, 30}]]//Flatten (* Harvey P. Dale, Dec 25 2019 *)

Prog

(PARI) a(n) = prod(i=1, n\2, if(isprime(i), i, 1)); \\ Altug Alkan, Mar 16 2018

Crossrefs

Cf. A002110, A054541, A056172, A089026.

Sequence in context: A350657 A140219 A259225 * A077081 A084700 A122766

Adjacent sequences: A300948 A300949 A300950 * A300952 A300953 A300954

Keyword

nonn

Author

Peter Luschny, Mar 16 2018

Status

approved