A080693 Numbers of the form p^2*q + r*s where p,q,r,s are (not necessarily distinct) primes.

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

Offset: 1

Author

Mario Maqueda Garcia [Garci'a] (israelmira(AT)terra.es), Mar 03 2003

Keywords

• nonn

Comments

A conjecture of Goldbach type says every number >= 26 is of this form.

Examples

			12=2^2*2 + 2*2
		

Crossrefs

Cf. A081053.

Programs

Maple

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:

Mathematica

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]

Extensions

Edited and extended by Robert G. Wilson v, Mar 05 2003