A072211 a(n) = p-1 if n=p, p if n=p^e and e<>1, 1 otherwise; p a prime.

1, 1, 2, 2, 4, 1, 6, 2, 3, 1, 10, 1, 12, 1, 1, 2, 16, 1, 18, 1, 1, 1, 22, 1, 5, 1, 3, 1, 28, 1, 30, 2, 1, 1, 1, 1, 36, 1, 1, 1, 40, 1, 42, 1, 1, 1, 46, 1, 7, 1, 1, 1, 52, 1, 1, 1, 1, 1, 58, 1, 60, 1, 1, 2, 1, 1, 66, 1, 1, 1, 70, 1, 72, 1, 1, 1, 1, 1, 78, 1, 3, 1, 82, 1, 1, 1, 1, 1, 88, 1, 1, 1, 1, 1

Offset: 1

Author

Vladeta Jovovic, Jul 03 2002

Keywords

• nonn

Comments

Product_{d divides n} a(d) = phi(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010.

Programs

Haskell

a072211 n = a072211_list !! (n-1)
a072211_list = 1 : zipWith div (tail a217863_list) a217863_list
-- Reinhard Zumkeller, Nov 24 2012

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 *)

PARI

a(n) = pp = isprimepower(n, &p); if (pp==1, n-1, if (pp, p, 1)); \\ Michel Marcus, Aug 25 2015

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