Search: id:A109470
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%I A109470
%S A109470 2,5,9,14,20,27,36,46,57,69,82,96,111,127,144,162,181,201,222,244,267,
%T A109470 291,316,342,370,399,429,460,492,525,559,594,630,667,705,744,784,825,
%U A109470 867,910,954,999,1045,1092,1140,1189,1239,1290,1342,1395,1449,1504,1560
%N A109470 Sum of first n non-cubes.
%C A109470 1^3 + 2^3 + 3^3 +...+ n^3=(1+2+3+...+n)^2. Note that the sum of noncubes 
               can be cube: a(6) = 3^3. Note that the sum of noncubes can be square: 
               a(4) = 3^2, a(7) = 6^2, a(15) = 12^2, a(37) = 28^2, a(69) = 51^2. 
               Primes in this sequence include: a(1) = 2, a(2) = 5, a(14) = 127, 
               a(17) = 181, a(62) = 2111, a(73) = 2903, a(77) = 3221.
%F A109470 a(n) = SUM{from i = 1 to n} A007412(i). a(n) = SUM{from i = 1 to n} (i 
               +[(i+[i^{1/3}])^{1/3}]) where [x] = floor(x). a(n) = A000217(A007412(n)) 
               - SUM{from i = 1 to [(A007412(n)^(1/3))]} i^3. a(n) = A000217(A007412(n)) 
               - (A000217([(A007412(n))^(1/3)])^2).
%F A109470 Set R=a007412(n), S=FLOOR(R^(1/3)), then a(n)=(R*(R+1))/2-((S*(S+1))/
               2)^2 [From Gerald Hillier (adr.rabbicat(AT)gmail.com), Dec 21 2008]
%e A109470 a(6) = 2 + 3 + 4 + 5 + 6 + 7 = 27.
%e A109470 a(7) = 2 + 3 + 4 + 5 + 6 + 7 + 9 = 36.
%Y A109470 Cf. A000537, A007412, A048766, A064524, A086849.
%Y A109470 Sequence in context: A080956 A132337 A134189 this_sequence A112873 A048093 
               A024669
%Y A109470 Adjacent sequences: A109467 A109468 A109469 this_sequence A109471 A109472 
               A109473
%K A109470 easy,nonn
%O A109470 1,1
%A A109470 Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 28 2005

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