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A173256 Partial sums of A001481. 1
0, 1, 3, 7, 12, 20, 29, 39, 52, 68, 85, 103, 123, 148, 174, 203, 235, 269, 305, 342, 382, 423, 468, 517, 567, 619, 672, 730, 791, 855, 920, 988, 1060, 1133, 1207, 1287, 1368, 1450, 1535, 1624, 1714, 1811, 1909, 2009, 2110, 2214, 2320, 2429, 2542, 2658, 2775 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The subsequence of primes in this sequence begins 3, 7, 29, 103, 269, 619, 1811, 3271.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = SUM[i=1..n] A001481(i) = SUM[i=1..n] (numbers that are the sum of 2 nonnegative squares) = SUM[i=1..n] (numbers n such that i = x^2 + y^2 has a solution in nonnegative integers x, y).

EXAMPLE

a(66) = 0 + 1 + 2 + 4 + 5 + 8 + 9 + 10 + 13 + 16 + 17 + 18 + 20 + 25 + 26 + 29 + 32 + 34 + 36 + 37 + 40 + 41 + 45 + 49 + 50 + 52 + 53 + 58 + 61 + 64 + 65 + 68 + 72 + 73 + 74 + 80 + 81 + 82 + 85 + 89 + 90 + 97 + 98 + 100 + 101 + 104 + 106 + 109 + 113 + 116 + 117 + 121 + 122 + 125 + 128 + 130 + 136 + 137 + 144 + 145 + 146 + 148 + 149 + 153 + 157 + 160.

MAPLE

N:= 1000:

A001481:= sort(convert({seq(seq(x^2+y^2, y=0..floor(sqrt(N-x^2))), x=0..floor(sqrt(N)))}, list)):

ListTools:-PartialSums(A001481); # Robert Israel, Mar 15 2016

CROSSREFS

Cf. A001481, A022544, A004018, A000161, A002654, A064533, A000404, A002828, A000378, A025284-A025320, A125110, A091072.

Sequence in context: A279169 A132273 A130050 * A330285 A002049 A025582

Adjacent sequences:  A173253 A173254 A173255 * A173257 A173258 A173259

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Feb 14 2010

EXTENSIONS

a(21) corrected by Robert Israel, Mar 15 2016

STATUS

approved

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Last modified February 21 18:04 EST 2020. Contains 332105 sequences. (Running on oeis4.)