A164914 a(n) = A164853(n+1)/A164853(n).

3, 3, 5, 7, 1, 1, 11, 5, 13, 1, 17, 1, 19, 1, 23, 7, 1, 1, 1, 29, 31, 1, 1, 37, 1, 41, 1, 43, 1, 1, 1, 47, 1, 53, 1, 1, 59, 1, 11, 61, 1, 1, 1, 67, 1, 71, 1, 1, 73, 1, 79, 1, 1, 83, 13, 1, 89, 1, 1, 1, 97, 1, 101, 1, 1, 103, 1, 1, 107, 1, 1, 109, 1, 1, 113, 1, 1, 1, 1, 1, 127, 1, 131, 1, 1, 137

Offset

1,1

Comments

Or, lcm(first n+1 semiprimes) / lcm(first n semiprimes).

All terms are 1 or prime.

a(n) = p if A001358(n+1) is 2*p or p^2 where p is prime, otherwise a(n)=1. - Robert Israel, May 31 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

N:= 1000: # to use the semiprimes <= N
P:= select(isprime, [2, seq(i, i=3..N/2, 2)]):
S:= sort(convert({seq(op(p*select(`<=`, P, N/p)), p=P)}, list)):
map(proc(t) if issqr(t) then sqrt(t) elif t::even then t/2 else 1 fi end proc, S[2..-1]); # Robert Israel, May 31 2018

Mathematica

A164853 = With[{s = Select[Range[1000], PrimeOmega[#] == 2&]}, Table[LCM @@ Take[s, n], {n, Length[s]}]];
Rest@A164853 / Most@A164853 (* Jean-François Alcover, Aug 28 2020, after Harvey P. Dale in A164853 *)

Crossrefs

Cf. A001358, A164853.

Sequence in context: A095950 A089874 A092035 * A247479 A134855 A335045

Adjacent sequences: A164911 A164912 A164913 * A164915 A164916 A164917

Keyword

nonn

Author

Zak Seidov and Jonathan Vos Post, Aug 31 2009

Status

approved