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

Author

Peter Luschny, Mar 16 2018

Keywords

• nonn

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

Crossrefs

Cf. A002110, A054541, A056172, A089026.

Programs

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 *)

PARI

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

Formula

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