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A124786 Numbers n such that n, sopfr(n) and sopfr(sopfr(n)) are all semiprimes.

%I A124786 #11 Jul 20 2024 06:53:42
%S A124786 4,14,33,38,46,49,62,69,94,129,133,134,166,169,177,205,213,217,254,
%T A124786 262,309,334,361,393,422,445,469,489,493,502,505,526,529,614,669,718,
%U A124786 753,793,817,865,886,889,913,933,934,961,974,982,993,1006,1077,1126,1142
%N A124786 Numbers n such that n, sopfr(n) and sopfr(sopfr(n)) are all semiprimes.
%C A124786 Cf. A001358 semiprimes, A001414 sopfr, A115585 Semiprimes with a semiprime sum of factors, A124785(n)=sopfr(A115585(n)).
%e A124786 Full table of {n, sopfr(n), sopfr(sopfr(n))}:
%e A124786 {4, 4, 4}, {14, 9, 6}, {33, 14, 9}, {38, 21, 10}, {46, 25, 10}, {62, 33, 14}, {69, 26, 15}, {94, 49, 14}, {129, 46, 25}, {134, 69, 26}, {166, 85, 22}, {177, 62, 33}, {213, 74, 39}, {217, 38, 21}, {254, 129, 46}, {262, 133, 26}, {309, 106, 55}, {334, 169, 26}, {393, 134, 69}, {422, 213, 74}, {445, 94, 49}, {489, 166, 85}, {502, 253, 34}, {526, 265, 58}.
%p A124786 isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true ; else false ; fi ; end: A001414 := proc(n) local ifs; if n = 1 then 0; else ifs := ifactors(n)[2] ; add( op(1,i)*op(2,i),i=ifs) ; fi ; end: A081758 := proc(n) A001414(A001414(n)) ; end: isA124786 := proc(n) if isA001358(n) and isA001358(A001414(n)) and isA001358(A081758(n)) then true ; else false ; fi ; end: for n from 2 to 2000 do if isA124786(n) then printf("%d, ",n) ; fi : od: # _R. J. Mathar_, Sep 23 2007
%t A124786 semiprimeQ[n_] := PrimeOmega[n] == 2;
%t A124786 sopfr[n_] := Total[Times @@@ FactorInteger[n]];
%t A124786 okQ[n_] := semiprimeQ[n] && semiprimeQ[ sopfr[n]] && semiprimeQ[ sopfr@ sopfr@n];
%t A124786 Select[Range[2000], okQ] (* _Jean-François Alcover_, Jul 20 2024 *)
%Y A124786 Cf. A001358, A001414, A115585, A124785.
%K A124786 nonn
%O A124786 1,1
%A A124786 _Zak Seidov_, Nov 07 2006
%E A124786 Corrected and extended by _R. J. Mathar_, Sep 23 2007