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A125112
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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;
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MAPLE
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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
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MATHEMATICA
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isA000408[n_] := Module[{a, b, c2}, a = 1; While[a^2 < n, b = 1; While[b <= a && a^2 + b^2 < n, c2 = n - a^2 - b^2; If[IntegerQ@Sqrt@c2, Return[True]]; b++]; a++]; Return[False]];
isA125112[n_] := Module[{d, i}, If[isA000408[n], Return[False], d = Divisors[n]; For[i = 1, i <= Length[d], i++, If[isA000408[d[[i]]] && isA000408[n/d[[i]]], Return[True]]]; Return[False]]];
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CROSSREFS
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Cf. A000408 (sums of 3 nonzero squares), A004214 (not sums of 3 nonzero squares).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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