



1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 5, 1, 3, 3, 1, 1, 1, 3, 9, 1, 3, 5, 11, 1, 5, 3, 9, 3, 7, 1, 15, 1, 5, 1, 3, 3, 9, 9, 3, 1, 5, 3, 21, 5, 3, 11, 23, 1, 21, 5, 1, 3, 13, 9, 5, 3, 9, 7, 29, 1, 15, 15, 9, 1, 3, 5, 33, 1, 11, 3, 35, 3, 9, 9, 5, 9, 15, 3, 39, 1, 27, 5, 41, 3, 1, 21, 7, 5, 11, 3, 9, 11, 15, 23
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OFFSET

1,7


COMMENTS

This is not necessarily the squarefree kernel. E.g., for n=19, phi(19)=18 is divisible by 9, an odd square. Values at which this kernel is 1 correspond to A003401 (polygons constructible with ruler and compass).
Multiplicative with a(2^e) = 1, a(p^e) = p^(e1)*A000265(p1).  Christian G. Bower, May 16 2005


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


EXAMPLE

n = 70 = 2*5*7, phi(70) = 24 = 8*3, so the odd kernel of 70 is a(70)=3.


MATHEMATICA

f1[x_] :=x/(Part[Flatten[FactorInteger[x]], 1]^ Part[Flatten[FactorInteger[x]], 2]); ta=Table[0, {100}]; g[x_] :=(1Mod[x, 2])*f1[x]+Mod[x, 2]*x; j=1; Do[Print[g[EulerPhi[n]]]; ta[[j]]=g[EulerPhi[n]]; j=j+1, {n, 2, 100}]; ta


PROG

(PARI) a(n)=n=eulerphi(n); n>>valuation(n, 2) \\ Charles R Greathouse IV, Mar 05 2013
(Haskell)
a053575 = a000265 . a000010  Reinhard Zumkeller, Oct 09 2013


CROSSREFS

Cf. A000010, A000265.
Cf. A227944.
Sequence in context: A095660 A035648 A213621 * A250207 A216319 A218355
Adjacent sequences: A053572 A053573 A053574 * A053576 A053577 A053578


KEYWORD

nonn,mult


AUTHOR

Labos Elemer, Jan 18 2000


STATUS

approved



