A109770 Partial sums of A011757.

2, 9, 32, 85, 182, 333, 560, 871, 1290, 1831, 2492, 3319, 4328, 5521, 6948, 8567, 10446, 12589, 15026, 17767, 20850, 24311, 28114, 32325, 36962, 42013, 47532, 53539, 60020, 67017, 74590, 82751, 91488, 100829, 110760, 121387, 132708, 144757, 157500, 170999, 185326

Offset

1,1

Links

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

Formula

a(n) = Sum_{k=1..n} prime(k^2).

Example

a(1) = 2 = prime(1^2).
a(2) = 9 = 2 + 7 = prime(1^2) + prime(2^2).
a(3) = 32 = 2 + 7 + 23 = prime(1^2) + prime(2^2) + prime(3^2).
a(4) = 85 = 2 + 7 + 23 + 53 = prime(1^2) + prime(2^2) + prime(3^2) + prime(4^2).

Mathematica

Accumulate[Prime[Range[40]^2]] (* Harvey P. Dale, May 31 2014 *)

Prog

(Magma)
[n le 1 select 2 else Self(n-1) +NthPrime(n^2): n in [1..50]]; // G. C. Greubel, Nov 15 2025
(SageMath)
def A109770(n): return 0 if n==0 else A109770(n-1) + nth_prime(n^2)
print([A109770(n) for n in range(1, 51)]) # G. C. Greubel, Nov 15 2025

Crossrefs

Cf. A011757.

Sequence in context: A165653 A182265 A212873 * A242512 A198016 A082114

Adjacent sequences: A109767 A109768 A109769 * A109771 A109772 A109773

Keyword

nonn

Author

Jonathan Vos Post, Aug 13 2005

Status

approved