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a(n) is the central prime factor of A046339(n).
1

%I #7 Mar 03 2019 02:16:40

%S 2,2,3,2,3,2,3,2,3,2,3,2,5,2,3,3,2,5,2,5,2,3,2,2,7,3,3,5,3,5,2,3,2,3,

%T 2,2,5,2,5,3,7,2,3,7,3,2,5,2,5,3,2,3,5,2,3,7,3,2,5,2,5,2,3,2,2,3,5,7,

%U 2,7,11,3,2,7,3,3,5,3,3,2,7,2,3,2,7,5,3,2,3,2,5,11,2,5,2,3,2,5,2,2,3,2,7,5

%N a(n) is the central prime factor of A046339(n).

%e a(8)=2 since A046339(8) = 32 = 2*2*2*2*2.

%e a(9)=3 since A046339(9) = 42 = 2*3*7.

%e a(10)=2 since A046339(10) = 44 = 2*2*11.

%e a(11)=3 since A046339(11) = 45 = 3*3*5.

%e a(12)=2 since A046339(12) = 48 = 2*2*2*2*3.

%p cpr := proc(n) nred := n ; while numtheory[bigomega](nred) > 1 do pf := sort(convert(numtheory[factorset](nred), list)) ; nred := nred/op(1, pf)/op(-1, pf) ; od: nred ; end:

%p A046339 := proc(n) option remember ; if n = 1 then 8 ; else for a from procname(n-1)+1 do if not isprime(a) and numtheory[bigomega](a) mod 2 = 1 then RETURN(a) ; fi; od: fi; end:

%p A163178 := proc(n) cpr(A046339(n)) ; end; seq(A163178(n), n=1..120) ; # _R. J. Mathar_, Jul 25 2009

%Y Cf. A046339, A162361.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jul 22 2009

%E More terms from _R. J. Mathar_, Jul 25 2009