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A108182 Cumulative sum of antisquares (A080255). 0

%I #12 Jun 18 2016 11:14:00

%S 6,16,31,52,74,98,124,157,192,230,270,312,363,417,474,532,592,657,723,

%T 792,862,936,1013,1091,1175,1260,1346,1433,1521,1611,1702,1795,1891,

%U 1993,2097,2202,2308,2418,2532,2647,2765,2884,3006,3129,3258,3390,3523,3657

%N Cumulative sum of antisquares (A080255).

%C 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?

%C 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.

%C 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AntisquareNumber.html">Antisquare Number</a>.

%F a(n) = Sum_{k=1..n} A080255(k).

%e 6 and 10 are the first two antisquares, so a(1)=6 and a(2)=16.

%Y Cf. A080255.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Jul 23 2005

%E Missing a(5) from _Giovanni Resta_, Jun 18 2016

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