A189997 Partial sums of A061742.

1, 5, 41, 941, 45041, 5381141, 907182041, 261527642141, 94345513738241, 49864774158575141, 41906795264466408041, 40266416996450293824941, 55107620882419848027561041, 92623330477259151438437945141, 171251267391917835862107238146041

Offset: 0

Author

Jonathan Vos Post, May 03 2011

Keywords

• nonn
• easy

Comments

Sum of squares of products of first n primes. The subsequence of primes begins: 5, 41, 941, 5381141, ...

a(n) is prime for n = 1, 2, 3, 5, 13, 51, 80, 342, 1754, and no other value below 3000. - Amiram Eldar, Nov 11 2017

Examples

			a(13) = 1 + 4 + 36 + 900 + 44100 + 5336100 + 901800900 + 260620460100 + 94083986096100 + 49770428644836900 + 41856930490307832900, 40224510201185827416900 + 55067354465423397733736100 + 92568222856376731590410384100.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..195

Crossrefs

Cf. A000040, A002110, A061742.

Programs

Mathematica

primorial[n_] := Product[Prime[i], {i, n}]; a[n_] := Sum[primorial[k]^2, {k, 1, n}]; Table[a[n] + 1, {n, 0, 15}] (* Amiram Eldar, Nov 11 2017 *)

Formula

Sum_{i=0..n} A061742(i) = Sum_{i=0..n} A002110(i)^2.

Extensions

Some terms corrected by Amiram Eldar, Nov 11 2017