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

1,1

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A343556 A319396 A049237 * A171135 A073855 A306312

Adjacent sequences: A162358 A162359 A162360 * A162362 A162363 A162364

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 02 2009

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

Status

approved