A185952 Partial products of A002313, the primes that are 1 or 2 (mod 4).

2, 10, 130, 2210, 64090, 2371330, 97224530, 5152900090, 314326905490, 22945864100770, 2042181904968530, 198091644781947410, 20007256122976688410, 2180790917404459036690, 246429373666703871145970

Offset: 1

Author

Jonathan Vos Post, Feb 07 2011

Keywords

• nonn
• easy

Comments

Product of the first n primes which are natural primes which are not Gaussian primes. Product of the first n primes congruent to 1 or 2 modulo 4. Product of the first n primes of form x^2+y^2. Product of the first n primes p such that -1 is a square mod p. Factors of primorials (A002110) not divisible by natural primes which are also Gaussian primes.

Essentially twice A006278.

Examples

			a(10) = 2 * 5 * 13 * 17 * 29 * 37 * 41 * 53 * 61 * 73 = 22945864100770.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A000040, A002110, A002313, A042963, A103222.

Programs

Mathematica

Rest@ FoldList[#1*#2 &, 1, Select[ Prime@ Range@ 30, Mod[#, 4] != 3 &]] (* Robert G. Wilson v *)

PARI

pp(v)=my(t=1); vector(#v,i,t*=v[i])
pp(select(n->n%4<3, primes(20))) \\ Charles R Greathouse IV, Apr 21 2015

Formula

a(n) = Product_{i=1..n} A002313(i) = 2 * Product_{i=1..n} {p in A000040 but p not in A002145} = Product_{i=1..n} {A000040 intersection A042963}.

Extensions

Terms corrected by Robert G. Wilson v, Feb 11 2011