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A162361 Central prime factor of A014612(n).

%I A162361 #20 Oct 07 2024 01:33:02
%S A162361 2,2,3,2,3,2,3,3,2,3,5,2,3,3,2,5,5,2,3,2,7,3,3,5,5,3,2,3,2,5,5,3,7,2,
%T A162361 3,7,2,5,5,3,2,3,5,7,3,2,5,5,3,2,3,5,7,2,7,11,2,7,3,5,3,3,7,2,7,5,3,3,
%U A162361 2,5,11,5,2,5,2,3,7,5,2,3,13,7,5,3,2,7,11,3,3,5,11,7,3,2,7,3,2,7,5,2,11,3,5
%N A162361 Central prime factor of A014612(n).
%H A162361 Michel Marcus, <a href="/A162361/b162361.txt">Table of n, a(n) for n = 1..10000</a>
%F A162361 a(n) = m/(A020639(m)*A006530(m)) where m = A014612(n). - _Michel Marcus_, Feb 25 2019
%e A162361 a(1)=2 since A014612(1) =  8 = 2*2*2.
%e A162361 a(2)=2 since A014612(2) = 12 = 2*2*3.
%e A162361 a(3)=3 since A014612(3) = 18 = 2*3*3.
%e A162361 a(4)=2 since A014612(4) = 20 = 2*2*5.
%e A162361 a(5)=3 since A014612(5) = 27 = 3*3*3.
%e A162361 a(6)=2 since A014612(6) = 28 = 2*2*7.
%e A162361 a(7)=3 since A014612(7) = 30 = 2*3*5.
%p A162361 A014612 := proc(n) option remember ; if n = 1 then 8 ; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 3 then RETURN(a) ; fi; od: fi; end:
%p A162361 A162361 := proc(n) tpr := A014612(n) ; pf := sort(convert(numtheory[factorset](tpr),list)) ; tpr/op(1,pf)/op(-1,pf) ; end:
%p A162361 seq(A162361(n),n=1..120) ; # _R. J. Mathar_, Jul 06 2009
%t A162361 f[n_] := With[{fi = FactorInteger[n][[All, 1]]}, n/(fi[[1]] fi[[-1]])];
%t A162361 f /@ Select[Range[500], PrimeOmega[#] == 3&] (* _Jean-François Alcover_, Aug 05 2022 *)
%o A162361 (PARI) isok(n) = bigomega(n)==3;
%o A162361 lista(nn) = {for (n=1, nn, if (isok(n), my(f=factor(n)[,1]); print1(n/(vecmin(f)*vecmax(f)), ", ")););} \\ _Michel Marcus_, Feb 25 2019
%Y A162361 Cf. A014612, A020639 (Lpf), A006530 (Gpf).
%K A162361 nonn
%O A162361 1,1
%A A162361 _Juri-Stepan Gerasimov_, Jul 02 2009
%E A162361 Edited (but not checked) by _N. J. A. Sloane_, Jul 05 2009
%E A162361 Corrected and extended by _R. J. Mathar_ and _Ray Chandler_, Jul 06 2009