A173256 Partial sums of A001481.

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

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 = 4876.

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

Prog

(Python)
from itertools import count, accumulate, islice
from sympy import factorint
def A173256_gen(): # generator of terms
    return accumulate(filter(lambda n:all(p & 3 != 3 or e & 1 == 0 for p, e in factorint(n).items()), count(0)))
A173256_list = list(islice(A173256_gen(), 30)) # Chai Wah Wu, Jun 27 2022

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