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%I #11 Feb 05 2016 20:37:31
%S 63,87,135,156,159,183,207,231,252,279,303,319,327,348,351,375,399,
%T 423,444,447,471,476,495,519,540,543,551,567,572,583,591,615,624,636,
%U 639,663,671,687,700,711,732,735,759,783,807,828,831,847,855,879,903,924
%N 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.
%C Intersection of A004214 with products of pairs of terms of A000408.
%H Chai Wah Wu, <a href="/A125112/b125112.txt">Table of n, a(n) for n = 1..10000</a>
%e a(2) = 87 = 3 * 29 = (1^2+1^2+1^2) * (4^2+3^2+2^2)
%e 87 does not have a partition as a sum x^2+y^2+z^2 with x,y,z>0
%e 63=3*21; 87=3*29; 135=3*45; 156=6*26; 572=22*26;
%p 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
%Y Cf. A000408 (sums of 3 nonzero squares), A004214 (not sums of 3 nonzero squares).
%K nonn
%O 1,1
%A _Artur Jasinski_, Nov 21 2006
%E Edited and extended by _R. J. Mathar_ and _Ray Chandler_, Nov 23 2006
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