A108182 Cumulative sum of antisquares (A080255).

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

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