

A108182


Cumulative sum of antisquares (A080255).


0



6, 16, 31, 52, 74, 98, 124, 157, 192, 230, 270, 312, 363, 417, 474, 532, 592, 657, 723, 792, 862, 936, 1013, 1091, 1175, 1260, 1346, 1433, 1521, 1611, 1702, 1795, 1891, 1993, 2097, 2202, 2308, 2418, 2532, 2647, 2765, 2884, 3006, 3129, 3258, 3390, 3523, 3657
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OFFSET

1,1


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..48.
Eric Weisstein's World of Mathematics, Antisquare Number.


FORMULA

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


EXAMPLE

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


CROSSREFS

Cf. A080255.
Sequence in context: A301679 A115007 A005891 * A244242 A092286 A301723
Adjacent sequences: A108179 A108180 A108181 * A108183 A108184 A108185


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jul 23 2005


EXTENSIONS

Missing a(5) from Giovanni Resta, Jun 18 2016


STATUS

approved



