%I #13 Sep 07 2024 08:53:47

%S 2,5,9,13,19,25,33,41,50,59,70,81,92,104,116,130,145,160,176,192,208,

%T 226,244,263,284,305,327,350,373,396,420,444,468,492,519,548,578,608,

%U 638,668,698,728,759,791,823,857,891,925,959,993,1029,1066,1103,1140

%N Partial sums of A111939 (= number of primes < semiprime(n)).

%C Perfect powers occur at the following terms:

%C a(3) = 9 = 3^2

%C a(6) = 25 = 5^2

%C a(12) = 81 = 3^4

%C a(74) = 2025 = 45^2

%C a(2072) = 1062961 = 1031^2

%C a(43881) = 392713489 = 19817^2

%C a(134249) = 3497963832 = 1518^3

%C a(372727) = 25930982961 = 161031^2

%C a(1196234) = 257007427681 = 506959^2

%C a(1449506) = 375159925009 = 612503^2

%C a(5226094) = 4704717169296 = 2169036^2

%C a(8342271) = 11846166214276 = 3441826^2

%C a(62507725) = 635490555087844 = 25208938^2

%C a(91695024) = 1356954402007044 = 36836862^2

%C No further perfect powers through a(10^8).

%H Amiram Eldar, <a href="/A122489/b122489.txt">Table of n, a(n) for n = 1..10000</a>

%t t=PrimePi@Select[Range@218, Plus @@ Last /@ FactorInteger@# == 2 &]; Table[Sum[t[[i]], {i, n}], {n, Length[t]}] (* _Ray Chandler_, Sep 20 2006 *)

%Y Partial sums of A111939.

%K easy,nonn

%O 1,1

%A _Giovanni Teofilatto_, Sep 16 2006

%E Edited and corrected by _Ray Chandler_, Sep 20 2006