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a(n) = floor(Sum_{k=1..n} sqrt(prime(k))).
3

%I #30 Feb 19 2024 10:31:06

%S 1,3,5,8,11,14,19,23,28,33,39,45,51,58,65,72,80,87,96,104,113,121,131,

%T 140,150,160,170,180,191,201,213,224,236,248,260,272,285,297,310,323,

%U 337,350,364,378,392,406,421,436,451,466,481,497,512,528,544,560,577

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

%H Harry J. Smith, <a href="/A062009/b062009.txt">Table of n, a(n) for n = 1..1000</a>

%t Table[Floor[Sum[Sqrt[Prime[i]], {i, n}]], {n, 100}] (* _Wesley Ivan Hurt_, Jan 28 2014 *)

%o (PARI) { default(realprecision, 100); for (n=1, 1000, write("b062009.txt", n, " ", floor(sum(k=1, n, sqrt(prime(k))))) ) } \\ _Harry J. Smith_, Jul 29 2009

%o (SageMath)

%o @CachedFunction

%o def b(n):

%o if (n==0): return 0

%o else: return b(n-1) + sqrt(nth_prime(n))

%o [floor(b(n)) for n in (1..100)] # _G. C. Greubel_, May 03 2022

%Y Cf. A062048.

%K easy,nonn

%O 1,2

%A _Jason Earls_, Jun 27 2001

%E Description corrected by _Dean Hickerson_, Jun 30 2001