%I #6 Jun 15 2016 08:59:58
%S 1,3,6,16,37,147,420,2290,7477,50487,200910,1534220,7099871,61765581,
%T 301088574,2870376944,15554495573,167142509403,940873745772,
%U 11097270672382,66032188454581,807449164097111,5147307668890832
%N Cumulative sum of double primorials (A079078).
%C The cumulative sum is prime for a(2) = 3, a(4) = 37, a(8) = 7477, a(12) = 7099871, a(16) = 15554495573. The sum a(n) is semiprime for n = 2, 9.
%F a(n) = 0## + 1## + ... + n##, where n## = p(n)*(n-2)##, where p(n) is the n-th prime.
%e n 0## + ... + n##
%e 0 1.
%e 1 1+2 = 3.
%e 2 1+2+3 = 6.
%e 3 1+2+3+10 = 16.
%e 4 1+2+3+10+21 = 37.
%e 5 1+2+3+10+21+110 = 147.
%e 6 1+2+3+10+21+110+273 = 420.
%e 7 1+2+3+10+21+110+273+1870 = 2290.
%e 8 1+2+3+10+21+110+273+1870+5187 = 7477.
%e 9 1+2+3+10+21+110+273+1870+5187+ 43010 = 50487.
%e 10 1+2+3+10+21+110+273+1870+5187+ 43010 + 150423 = 200910.
%t p[0]=1; p[1]=2; p[n_] := p[n] = Prime[n]*p[n - 2]; Accumulate[p /@ Range[0, 22]] (* _Giovanni Resta_, Jun 14 2016 *)
%Y Cf. A079078.
%K easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Feb 12 2006
%E Data corrected by _Giovanni Resta_, Jun 14 2016