A109818 Sum of primes between n and n^2.

0, 5, 15, 36, 95, 150, 318, 484, 774, 1043, 1576, 2099, 2886, 3790, 4620, 6040, 7941, 9465, 11541, 13810, 16763, 19982, 23515, 26840, 32253, 37461, 42368, 48394, 55737, 62668, 70112, 80029, 89512, 100678, 111427, 124051, 135954, 148630, 166354

Offset

1,2

Links

Table of n, a(n) for n=1..39.

Example

a(3) = 15 because 3, 5 and 7 are the A073882(3) = 3 primes in the interval from 3 to 3^2 inclusive and 3 + 5 + 7 = 15.

Mathematica

Join[{0}, Table[Sum[Prime[i], {i, If[PrimeQ[n], PrimePi[n], PrimePi[n]+1], PrimePi[n^2]}], {n, 2, 39}]] (* James C. McMahon, Apr 02 2024 *)

Prog

(PARI) for(n=1, 50, print1(sum(k=n, n^2, if(isprime(k), k)), ", "))

Crossrefs

Cf. A109819 (product of same primes), A073882 (number of primes between n and n^2).

Sequence in context: A111926 A369804 A137609 * A146797 A213487 A005491

Adjacent sequences: A109815 A109816 A109817 * A109819 A109820 A109821

Keyword

easy,nonn

Author

Rick L. Shepherd, Jul 02 2005

Status

approved