A062048 a(n) = Sum_{k=1..n} floor(sqrt(prime(k))).

1, 2, 4, 6, 9, 12, 16, 20, 24, 29, 34, 40, 46, 52, 58, 65, 72, 79, 87, 95, 103, 111, 120, 129, 138, 148, 158, 168, 178, 188, 199, 210, 221, 232, 244, 256, 268, 280, 292, 305, 318, 331, 344, 357, 371, 385, 399, 413, 428, 443, 458, 473, 488, 503, 519, 535, 551

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

a(n) = a(n-1) + floor(sqrt(prime(n))) with a(1) = 1. - G. C. Greubel, May 06 2022

Mathematica

Accumulate[Floor[Sqrt[#]]&/@Prime[Range[60]]] (* Harvey P. Dale, May 08 2013 *)

Prog

(PARI) a(n)=my(s); forprime(p=2, prime(n), s+=sqrtint(p)); s \\ Charles R Greathouse IV, Jan 06 2016
(SageMath)
def a(n): # a = A062048
    if (n==1): return 1
    else: return a(n-1) + floor(sqrt(nth_prime(n)))
[a(n) for n in (1..60)] # G. C. Greubel, May 06 2022

Crossrefs

Cf. A062009.

Partial sums of A000006.

Sequence in context: A145196 A061536 A095114 * A194174 A168048 A075354

Adjacent sequences: A062045 A062046 A062047 * A062049 A062050 A062051

Keyword

easy,nonn

Author

Dean Hickerson, Jun 30 2001

Status

approved