A162361 Central prime factor of A014612(n).

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, 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, 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

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 02 2009

Keywords

• nonn

Examples

			a(1)=2 since A014612(1) =  8 = 2*2*2.
a(2)=2 since A014612(2) = 12 = 2*2*3.
a(3)=3 since A014612(3) = 18 = 2*3*3.
a(4)=2 since A014612(4) = 20 = 2*2*5.
a(5)=3 since A014612(5) = 27 = 3*3*3.
a(6)=2 since A014612(6) = 28 = 2*2*7.
a(7)=3 since A014612(7) = 30 = 2*3*5.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014612, A020639 (Lpf), A006530 (Gpf).

Programs

Maple

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:
A162361 := proc(n) tpr := A014612(n) ; pf := sort(convert(numtheory[factorset](tpr),list)) ; tpr/op(1,pf)/op(-1,pf) ; end:
seq(A162361(n),n=1..120) ; # R. J. Mathar, Jul 06 2009

Mathematica

f[n_] := With[{fi = FactorInteger[n][[All, 1]]}, n/(fi[[1]] fi[[-1]])];
f /@ Select[Range[500], PrimeOmega[#] == 3&] (* Jean-François Alcover, Aug 05 2022 *)

PARI

isok(n) = bigomega(n)==3;
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

Formula

a(n) = m/(A020639(m)*A006530(m)) where m = A014612(n). - Michel Marcus, Feb 25 2019

Extensions

Edited (but not checked) by N. J. A. Sloane, Jul 05 2009

Corrected and extended by R. J. Mathar and Ray Chandler, Jul 06 2009