Search: id:A108182
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%I A108182
%S A108182 6,16,31,52,98,124,157,192,230,270,312,363,417,474,532,592,657,723,792,
%T A108182 862,936,1013,1091,1175,1260,1346,1433,1521,1611,1702,1795,1891,1993,
%U A108182 2097,2202,2308,2418,2532,2647,2765,2884,3006,3129,3258,3390,3523,3657
%N A108182 Cumulative sum of antisquares (A080255).
%C A108182 Note that a(2), the sum of the first two antisquares, is a square, as 
               is a(29) = 1521 = 3^2 * 13^2. When is the cumulative sum of antisquares 
               an antisquare? a(n) is prime for a(3) = 31, a(8) = 157, a(23) = 1013, 
               a(24) = 1091, a(28) = 1433, a(34) = 1993, a(40) = 2647, a(51) = 4073. 
               a(n) is semiprime for a(1) = 6 = 2 * 3, a(5) = 74 = 2 * 37, a(14) 
               = 417 = 3 * 139, a(19) = 723 = 3 * 241, a(21) = 862 = 2 * 431, a(27) 
               = 1346 = 2 * 673, a(32) = 1795 = 5 * 359, a(33) = 1891 = 31 * 61, 
               a(47) = 3523 = 13 * 271.
%H A108182 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AntisquareNumber.html">Antisquare Number</a>.
%F A108182 a(n) = SUM[from k = 1 to n] A080255(k).
%e A108182 a(20) = 792 because 6+10+15+21+22+24+26+33+35+38+40+42+51+54+57+58+60+65+66+69 
               = 792 = 2^3 * 3^2 * 11.
%Y A108182 Cf. A080255.
%Y A108182 Sequence in context: A115007 A005891 A092286 this_sequence A097118 A134465 
               A036488
%Y A108182 Adjacent sequences: A108179 A108180 A108181 this_sequence A108183 A108184 
               A108185
%K A108182 easy,nonn
%O A108182 1,1
%A A108182 Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 23 2005

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