A125112 Numbers which are not the sum of 3 nonzero squares, but which can be expressed as the product of two numbers that are the sum of 3 nonzero squares.

63, 87, 135, 156, 159, 183, 207, 231, 252, 279, 303, 319, 327, 348, 351, 375, 399, 423, 444, 447, 471, 476, 495, 519, 540, 543, 551, 567, 572, 583, 591, 615, 624, 636, 639, 663, 671, 687, 700, 711, 732, 735, 759, 783, 807, 828, 831, 847, 855, 879, 903, 924

Offset

1,1

Comments

Intersection of A004214 with products of pairs of terms of A000408.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

a(2) = 87 = 3 * 29 = (1^2+1^2+1^2) * (4^2+3^2+2^2)
87 does not have a partition as a sum x^2+y^2+z^2 with x,y,z>0
63=3*21; 87=3*29; 135=3*45; 156=6*26; 572=22*26;

Maple

isA000408 := proc(n) local a, b, c2 ; a:=1; while a^2<n do b:=1 ; while b<=a and a^2+b^2<n do c2 := n-a^2-b^2 ; if issqr(c2) then RETURN(true) ; fi ; b := b+1 ; od ; a := a+1 ; od ; RETURN(false) ; end: isA125112 := proc(n) local d, i; if isA000408(n) then RETURN(false) ; else d := numtheory[divisors](n) ; for i from 1 to nops(d) do if isA000408(op(i, d)) and isA000408(n/op(i, d)) then RETURN(true) ; fi ; od ; RETURN(false) ; fi ; end: for an from 1 to 1600 do if isA125112(an) then printf("%d, ", an) ; fi ; od ; # R. J. Mathar, Nov 23 2006

Crossrefs

Cf. A000408 (sums of 3 nonzero squares), A004214 (not sums of 3 nonzero squares).

Sequence in context: A320066 A372557 A372558 * A043186 A039363 A043966

Adjacent sequences: A125109 A125110 A125111 * A125113 A125114 A125115

Keyword

nonn

Author

Artur Jasinski, Nov 21 2006

Extensions

Edited and extended by R. J. Mathar and Ray Chandler, Nov 23 2006

Status

approved