A163178 a(n) is the central prime factor of A046339(n).
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, 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, 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
Offset: 1
Keywords
Examples
a(8)=2 since A046339(8) = 32 = 2*2*2*2*2. a(9)=3 since A046339(9) = 42 = 2*3*7. a(10)=2 since A046339(10) = 44 = 2*2*11. a(11)=3 since A046339(11) = 45 = 3*3*5. a(12)=2 since A046339(12) = 48 = 2*2*2*2*3.
Programs
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Maple
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: 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: A163178 := proc(n) cpr(A046339(n)) ; end; seq(A163178(n), n=1..120) ; # R. J. Mathar, Jul 25 2009
Extensions
More terms from R. J. Mathar, Jul 25 2009