

A180416


Number of positive integers below 10^n, excluding perfect squares, which have a representation as a sum of 2 positive squares.


6



3, 33, 298, 2649, 23711, 215341, 1982296, 18447847, 173197435, 1637524156, 15570196516, 148735628858, 1426303768587, 13722207893214, 132387231596281, 1280309591127436
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OFFSET

1,1


COMMENTS

Numbers that can be represented as a sum of three or more positive squares but not as a sum of two positive squares (e.g., 3=1^2+1^2+1^2 or 6=1^2+1^2+2^2) are not counted. Numbers that can be represented as a sum of two positive squares and alternatively as a sum of three or more positive squares are counted (e.g., 18 = 9+9 = 1+1+16, 26, 41, ...).


LINKS

Table of n, a(n) for n=1..16.
Eric W. Weisstein: MathWorld  Lagrange's FourSquare Theorem.
Eric W. Weisstein: MathWorld  Sum of Squares Function.


FORMULA

a(n) = { 0<k<10^n : k in {A000415} }.
a(n) = { 0<k<10^n : k in ({A000404} \ {A000290}) }.
a(n) = A002283(n)  A049416(n)  A167615(n)  A180425(n).


MAPLE

isA000415 := proc(n) local x , y2; if issqr(n) then false; else for x from 1 do y2 := nx^2 ; if y2 < x^2 then return false; elif issqr(y2) then return true; end if; end do ; end if; end proc:
A180416 := proc(n) a := 0 ; for k from 2 to 10^n1 do if isA000415(k) then a := a+1 ; end if; end do: a ; end proc:
for n from 1 do print(A180416(n)) ; end do; # R. J. Mathar, Jan 20 2011


CROSSREFS

Cf. A000415, A000404, A000290, A002283, A049416, A167613, A180425.
Sequence in context: A189644 A003129 A190542 * A043038 A274264 A107127
Adjacent sequences: A180413 A180414 A180415 * A180417 A180418 A180419


KEYWORD

nonn,more


AUTHOR

Martin Renner, Jan 19 2011


EXTENSIONS

a(6)a(8) from Alois P. Heinz, Jan 20 2011
a(9)a(10) from Donovan Johnson, Feb 04 2011
a(10) corrected and a(11)a(16) from Hiroaki Yamanouchi, Jul 13 2014


STATUS

approved



