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A080693
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Numbers of the form p^2*q + r*s where p,q,r,s are (not necessarily distinct) primes.
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0
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12, 14, 16, 17, 18, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86
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OFFSET
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1,1
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COMMENTS
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A conjecture of Goldbach type says every number >= 26 is of this form.
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LINKS
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EXAMPLE
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12=2^2*2 + 2*2
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MAPLE
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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:
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Mario Maqueda Garcia [Garci'a] (israelmira(AT)terra.es), Mar 03 2003
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EXTENSIONS
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STATUS
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approved
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