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Even terms in A100933.
3

%I #4 Jan 21 2014 12:30:21

%S 50,98,150,242,250,294,338,350,490,550,578,650,686,722,726,750,850,

%T 950,1014,1050,1058,1078,1150,1210,1274,1450,1470,1550,1650,1666,1682,

%U 1690,1694,1734,1750,1850,1862,1922,1950,2050,2058,2150,2166,2254,2350,2366

%N Even terms in A100933.

%p with(numtheory):

%p # For A100549: if n = prod_p p^e_p, then pp = largest prime <= 1 + max e_p

%p pp := proc(n) local f,m; option remember;

%p if (n = 1) then

%p return 1;

%p end if;

%p m := 1:

%p for f in op(2..-1,ifactors(n)) do

%p if (f[2] > m) then

%p m := f[2]:

%p end if;

%p end do;

%p prevprime(m+2);

%p end proc;

%p # For A100762: B = prod_{p <= pp(n)} p^e_p

%p B := proc(n) local v,f,pv; global pp; option remember;

%p pv := pp(n);

%p v := 1:

%p for f in op(2..-1,ifactors(n)) while f[1] <= pv do

%p v := v * f[1]^f[2];

%p end do;

%p return v;

%p end proc;

%p # For A100417: Bgood = (is pp(n) = pp(B(n))), that is, is B(n) enough to establish pp(n)?

%p Bgood := proc(n) global pp;

%p `if`(pp(B(n))=pp(n),true,false);

%p end proc;

%p # For A100933 and A141757:

%p t0:=select(not Bgood, [$1..3000]);

%p t1:=[];

%p for n from 1 to nops(t0) do

%p if t0[n] mod 2 = 0 then t1:=[op(t1),t0[n]]; fi; od: t1;

%K nonn

%O 1,1

%A _David Applegate_ and _N. J. A. Sloane_, Sep 15 2008