1,1

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;

# For A100933 and A141757:

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;

Sequence in context: A045165 A138381 A090997 this_sequence A044139 A044520 A158066

Adjacent sequences: A141754 A141755 A141756 this_sequence A141758 A141759 A141760

nonn

David Applegate and N. J. A. Sloane (njas(AT)research.att.com), Sep 15 2008