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Partial sums of A061742.
2

%I #16 Jan 12 2018 02:56:09

%S 1,5,41,941,45041,5381141,907182041,261527642141,94345513738241,

%T 49864774158575141,41906795264466408041,40266416996450293824941,

%U 55107620882419848027561041,92623330477259151438437945141,171251267391917835862107238146041

%N Partial sums of A061742.

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

%C 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

%H G. C. Greubel, <a href="/A189997/b189997.txt">Table of n, a(n) for n = 0..195</a>

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

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

%t 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 *)

%Y Cf. A000040, A002110, A061742.

%K nonn,easy

%O 0,2

%A _Jonathan Vos Post_, May 03 2011

%E Some terms corrected by _Amiram Eldar_, Nov 11 2017