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A112141 Product of the first n semiprimes. 17
4, 24, 216, 2160, 30240, 453600, 9525600, 209563200, 5239080000, 136216080000, 4495130640000, 152834441760000, 5349205461600000, 203269807540800000, 7927522494091200000, 364666034728195200000, 17868635701681564800000, 911300420785759804800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Semiprime analog of primorial (A002110). Equivalent for product of what A062198 is for sum. Bigomega(a(n)) = the number of not necessarily distinct prime factors of a(n) = A001222(a(n)) = A005843(n) = 2*n.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..100

FORMULA

a(n) = prod_{i=1..n} A001358(i).

EXAMPLE

a(10) = 4*6*9*10*14*15*21*22*25*26 = 136216080000, the product of the first 10 semiprimes.

MATHEMATICA

NextSemiPrime[n_, k_: 1] := Block[{c = 0, sgn = Sign[k]}, sp = n + sgn; While[c < Abs[k], While[ PrimeOmega[sp] != 2, If[sgn < 0, sp--, sp++]]; If[sgn < 0, sp--, sp++]; c++]; sp + If[sgn < 0, 1, -1]]; f[n_] := Times @@ NestList[ NextSemiPrime@# &, 2^2, n - 1]; Array[f, 18] (* Robert G. Wilson v, Jun 13 2013 *)

PROG

(PARI) a(n)=my(v=vector(n), i, k=3); while(i<n, if(bigomega(k++)==2, v[i++]=k)); prod(i=1, n, v[i]) \\ Charles R Greathouse IV, Apr 04 2013

CROSSREFS

Cf. A001358, A002110, A062198, A112141.

Sequence in context: A010039 A245407 A162314 * A077555 A166881 A183279

Adjacent sequences:  A112138 A112139 A112140 * A112142 A112143 A112144

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 28 2005

STATUS

approved

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Last modified December 11 05:41 EST 2017. Contains 295868 sequences.