OFFSET
1,3
COMMENTS
Product_{d divides n} a(d) = phi(n).
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = Product_{d divides n} phi(n/d)^mu(d). - Vladeta Jovovic, Mar 08 2004
a(n) = A217863(n)/A217863(n-1) for n > 1. - Eric Desbiaux, Nov 23 2012; corrected by Thomas Ordowski, Aug 25 2015
D.g.f.: zeta(s) + Sum_{p prime} (p-2+p^(-s))/(p^s-1), - Robert Israel, Aug 25 2015
MAPLE
f:= proc(n)
local P;
P:= numtheory:-factorset(n);
if nops(P) > 1 then 1
elif n = P[1] then P[1]-1
else P[1]
fi
end proc:
1, seq(f(n), n=2..100); # Robert Israel, Aug 25 2015
MATHEMATICA
Table[Which[PrimeQ@ n, n - 1, ! PrimeQ@ n && PrimePowerQ@ n,
First @@ FactorInteger@ n, True, 1], {n, 88}] (* Michael De Vlieger, Aug 25 2015 *)
PROG
(Haskell)
a072211 n = a072211_list !! (n-1)
a072211_list = 1 : zipWith div (tail a217863_list) a217863_list
-- Reinhard Zumkeller, Nov 24 2012
(PARI) a(n) = pp = isprimepower(n, &p); if (pp==1, n-1, if (pp, p, 1)); \\ Michel Marcus, Aug 25 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Jul 03 2002
STATUS
approved