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 A072211 a(n) = p-1 if n=p, p if n=p^e and e<>1, 1 otherwise; p a prime. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000010. Sequence in context: A027420 A116588 A069922 * A360825 A328925 A299020 Adjacent sequences: A072208 A072209 A072210 * A072212 A072213 A072214 KEYWORD nonn AUTHOR Vladeta Jovovic, Jul 03 2002 STATUS approved

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Last modified March 31 15:10 EDT 2023. Contains 361668 sequences. (Running on oeis4.)