A109312 Numbers q such that q^2 is a sum of n-th and (n+1)-st semiprimes for some n.
6, 10, 19, 22, 24, 28, 35, 38, 39, 43, 46, 49, 50, 62, 64, 83, 92, 96, 106, 110, 114, 120, 133, 136, 139, 142, 146, 168, 171, 172, 174, 180, 181, 199, 203, 204, 207, 208, 222, 230, 232, 240, 258, 276, 280, 288, 289, 294, 300, 304, 310, 321, 325, 326, 327, 328
Offset: 1
Keywords
Examples
6 is ok because sp(6)=15, sp(7)=21, 15+21=36=6^2, sp(n)=A001358(n)=n-th semiprime.
Crossrefs
Programs
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Maple
isA001358 := proc(n) option remember ; if numtheory[bigomega](n) = 2 then true; else false ; fi ; end: isA118717 := proc(n) option remember ; local qn,qn1 ; qn := 4 ; while true do qn1 := qn+1 ; while not isA001358(qn1) do qn1 := qn1+1 ; od ; if qn+qn1 =n then RETURN(true) ; elif qn+qn1 > n then RETURN(false) ; fi; qn := qn1 ; od; end: isA109312 := proc(q) isA118717(q^2) ; end: for q from 1 to 500 do if isA109312(q) then printf("%d,",q) ; fi ; od; # R. J. Mathar, Aug 15 2007
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Mathematica
Select[Sqrt[#]&/@(Total/@Partition[Select[Range[80000],PrimeOmega[#] == 2&],2,1]),IntegerQ] (* Harvey P. Dale, Dec 11 2018 *)
Formula
q^2=sp(n)+sp(n+1), sp(n)=n-th semiprime.
Extensions
More terms from R. J. Mathar, Aug 15 2007