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A098109
Number of divisors of a(n)! exceeds 10^n.
2
5, 9, 13, 17, 23, 29, 34, 40, 46, 53, 59, 67, 73, 79, 87, 95, 103, 109, 116, 127, 134, 141, 150, 158, 167, 175, 182, 193, 199, 210, 218, 227, 234, 242, 254, 263, 271, 281, 290, 301, 311, 317, 329, 337, 349, 358, 367, 379, 387, 397, 406, 418, 427, 436, 446, 455
OFFSET
1,1
MAPLE
# multiply two ifactor representations [p1, e1], [p2, e2], [p3, e2]
mulif := proc(if1, if2)
local ifr, t, p, e, ix, ifi ;
ifr := if1 ;
for t in if2 do
p := op(1, t) ;
e := op(2, t) ;
ix := 0 ;
for ifi from 1 to nops(ifr) do
if op(1, op(ifi, ifr)) = p then
ix := ifi;
break;
end if;
end do:
if ix = 0 then
ifr := [op(ifr), [p, e]] ;
else
e := e+op(2, op(ix, ifr)) ;
ifr := subsop(ix=[p, e], ifr) ;
end if;
end do:
return ifr ;
end proc:
# tau(iff) using multiplicative property of tau
tauif := proc(iff)
local r;
r := 1 ;
for t in iff do
r := r*(1+op(2, t)) ;
end do:
return r;
end proc:
# ifactor representation of m!
iffact := proc(m)
local r, f ;
if m <=1 then
return [] ;
else
r := [[2, 1]] ;
for f from 3 to m do
ifmf := ifactors(f)[2] ;
r := mulif(r, ifmf) ;
end do:
return r;
end if:
end proc:
A027423 := proc(n)
iffact(n) ;
tauif(%) ;
end proc:
A098109 := proc(n)
local m ;
for m from 2 do
if A027423(m) > 10^n then
return m;
end if;
end do:
end proc:
for n from 1 do
print(A098109(n)) ;
end do: # R. J. Mathar, Nov 19 2011
CROSSREFS
Cf. A027423.
Sequence in context: A314691 A314692 A314693 * A314694 A314695 A314696
KEYWORD
nonn
AUTHOR
Jeff Burch, Sep 23 2004
STATUS
approved