A116367 Sums of rows of the triangle in A116366.

6, 18, 36, 70, 104, 158, 208, 282, 388, 468, 602, 728, 838, 984, 1174, 1382, 1536, 1772, 1986, 2170, 2448, 2698, 3008, 3386, 3684, 3940, 4258, 4530, 4868, 5528, 5910, 6370, 6712, 7340, 7710, 8234, 8776, 9258, 9832, 10424, 10866, 11658, 12128, 12694, 13180

Offset: 1

Author

Reinhard Zumkeller, Feb 06 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Programs

GAP

List([1..50], n-> Sum([1..n], k-> Primes[n+1] + Primes[k+1])); # G. C. Greubel, May 18 2019

Magma

[(&+[NthPrime(n+1) + NthPrime(k+1): k in [1..n]]): n in [1..50]]; // G. C. Greubel, May 18 2019

Mathematica

Table[Sum[Prime[n+1] + Prime[k+1], {k,1,n}], {n,1,50}] (* G. C. Greubel, May 18 2019 *)

PARI

vector(50, n, sum(k=1,n, prime(n+1) + prime(k+1))) \\ G. C. Greubel, May 18 2019

Sage

[sum(nth_prime(n+1) + nth_prime(k+1) for k in (1..n)) for n in (1..50)] # G. C. Greubel, May 18 2019

Formula

a(n) = Sum_{k=1..n} A116366(n,k).

a(n) = (n+1)*A000040(n+1) + A007504(n) - 2.