A114410 Cumulative sum of double primorials (A079078).

1, 3, 6, 16, 37, 147, 420, 2290, 7477, 50487, 200910, 1534220, 7099871, 61765581, 301088574, 2870376944, 15554495573, 167142509403, 940873745772, 11097270672382, 66032188454581, 807449164097111, 5147307668890832

Offset: 0

Author

Jonathan Vos Post, Feb 12 2006

Keywords

• easy
• nonn

Comments

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.

Examples

			n 0## + ... + n##
0 1.
1 1+2 = 3.
2 1+2+3 = 6.
3 1+2+3+10 = 16.
4 1+2+3+10+21 = 37.
5 1+2+3+10+21+110 = 147.
6 1+2+3+10+21+110+273 = 420.
7 1+2+3+10+21+110+273+1870 = 2290.
8 1+2+3+10+21+110+273+1870+5187 = 7477.
9 1+2+3+10+21+110+273+1870+5187+ 43010 = 50487.
10 1+2+3+10+21+110+273+1870+5187+ 43010 + 150423 = 200910.
		

Crossrefs

Cf. A079078.

Programs

Mathematica

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 *)

Formula

a(n) = 0## + 1## + ... + n##, where n## = p(n)*(n-2)##, where p(n) is the n-th prime.

Extensions

Data corrected by Giovanni Resta, Jun 14 2016