%I #26 Jul 30 2021 02:04:29

%S 5,12,24,59,60,168,173,290,269,533,534,787,917,830,1420,1901,1541,

%T 2076,2288,2953,3219,3533,3348,5413,5208,4907,6026,7343,6960,7444,

%U 9948,9483,11166,10749,12624,11903,12713,17724,17155,19590,18975,16249,22702,21859,26943

%N Sum of primes p with n^2 < p < (n+1)^2.

%H Michael S. Branicky, <a href="/A108314/b108314.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)

%e a(2)=12 because between 4 and 9 there are two primes (5 and 7) with sum equal to 12.

%p a:=proc(n) local s,j: s:=0: for j from n^2 to (n+1)^2 do if isprime(j)=true then s:=s+j else s:=s: fi od end: seq(a(n),n=1..50); # _Emeric Deutsch_, Jul 01 2005

%t f[n_] := Plus @@ Prime[ Range[PrimePi[n^2] + 1, PrimePi[(n + 1)^2]]]; Table[ f[n], {n, 44}] (* _Robert G. Wilson v_, Jul 01 2005 *)

%o (PARI) A108314(n)={r=0;forprime(i=n^2+1,(n+1)^2-1,r=r+i);r} \\ _Michael B. Porter_, Oct 14 2009

%o (Python)

%o from sympy import sieve

%o def a(n): return sum(p for p in sieve.primerange(n**2, (n+1)**2))

%o print([a(n) for n in range(1, 46)]) # _Michael S. Branicky_, Jul 29 2021

%Y Cf. A014085, A158528, A293697.

%K easy,nonn

%O 1,1

%A _Giovanni Teofilatto_, Jun 30 2005

%E Edited, corrected and extended by _Emeric Deutsch_, _Robert G. Wilson v_ and _Rick L. Shepherd_, Jul 01 2005