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

Author

Zak Seidov, Nov 07 2006

Keywords

• nonn

Comments

Cf. A001358 semiprimes, A001414 sopfr, A115585 Semiprimes with a semiprime sum of factors, A124785(n)=sopfr(A115585(n)).

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}.
		

Crossrefs

Cf. A001358, A001414, A115585, A124785.

Programs

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

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