OFFSET
1,1
MAPLE
with(numtheory):
# For A100549: if n = prod_p p^e_p, then pp = largest prime <= 1 + max e_p
pp := proc(n) local f, m; option remember;
if (n = 1) then
return 1;
end if;
m := 1:
for f in op(2..-1, ifactors(n)) do
if (f[2] > m) then
m := f[2]:
end if;
end do;
prevprime(m+2);
end proc;
# For A100762: B = prod_{p <= pp(n)} p^e_p
B := proc(n) local v, f, pv; global pp; option remember;
pv := pp(n);
v := 1:
for f in op(2..-1, ifactors(n)) while f[1] <= pv do
v := v * f[1]^f[2];
end do;
return v;
end proc;
# For A100417: Bgood = (is pp(n) = pp(B(n))), that is, is B(n) enough to establish pp(n)?
Bgood := proc(n) global pp;
`if`(pp(B(n))=pp(n), true, false);
end proc;
t0:=select(not Bgood, [$1..3000]);
t1:=[];
for n from 1 to nops(t0) do
if t0[n] mod 2 = 0 then t1:=[op(t1), t0[n]]; fi; od: t1;
CROSSREFS
KEYWORD
nonn
AUTHOR
David Applegate and N. J. A. Sloane, Sep 15 2008
STATUS
approved