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%I #3 Mar 30 2012 17:30:54
%S 12,14,16,17,18,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
%T 40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,
%U 63,64,65,66,67,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86
%N Numbers of the form p^2*q + r*s where p,q,r,s are (not necessarily distinct) primes.
%C A conjecture of Goldbach type says every number >= 26 is of this form.
%e 12=2^2*2 + 2*2
%p H := proc(n::posint) local p,q,r,s; p := 2; while p<=floor(sqrt((n-4)/2)) do q := 2; while q<=floor((n-4)/p^2) do s := 2; while s<=floor((n-p^2*q)/2) do r := (n-p^2*q)/s; if type(r,posint) then if isprime(r) then return(true,p,q,s,r); end if; end if; s := nextprime(s); end do; q := nextprime(q); end do; p := nextprime(p); end do; return(false); end:
%t Take[ Union[ Flatten[ Table[ Prime[p]^2*Prime[q] + Prime[r]*Prime[s], {p, 1, 6}, {q, 1, 15}, {r, 1, 15}, {s, 1, 15}]]], 70]
%Y Cf. A081053.
%K nonn
%O 1,1
%A Mario Maqueda Garcia [Garci'a] (israelmira(AT)terra.es), Mar 03 2003
%E Edited and extended by _Robert G. Wilson v_, Mar 05 2003
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