A124786 Numbers n such that n, sopfr(n) and sopfr(sopfr(n)) are all semiprimes.
4, 14, 33, 38, 46, 49, 62, 69, 94, 129, 133, 134, 166, 169, 177, 205, 213, 217, 254, 262, 309, 334, 361, 393, 422, 445, 469, 489, 493, 502, 505, 526, 529, 614, 669, 718, 753, 793, 817, 865, 886, 889, 913, 933, 934, 961, 974, 982, 993, 1006, 1077, 1126, 1142
Offset: 1
Keywords
Examples
Full table of {n, sopfr(n), sopfr(sopfr(n))}:
{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}.
Programs
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Maple
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
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Mathematica
semiprimeQ[n_] := PrimeOmega[n] == 2; sopfr[n_] := Total[Times @@@ FactorInteger[n]]; okQ[n_] := semiprimeQ[n] && semiprimeQ[ sopfr[n]] && semiprimeQ[ sopfr@ sopfr@n]; Select[Range[2000], okQ] (* Jean-François Alcover, Jul 20 2024 *)
Extensions
Corrected and extended by R. J. Mathar, Sep 23 2007
Comments