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A053575 Odd part of phi(n): a(n) = A000265(A000010(n)). 4
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 (list; graph; refs; listen; history; text; internal format)
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^(e-1)*A000265(p-1). 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 a(70)=3

MATHEMATICA

f1[x_] :=x/(Part[Flatten[FactorInteger[x]], 1]^ Part[Flatten[FactorInteger[x]], 2]); ta=Table[0, {100}]; g[x_] :=(1-Mod[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 * A216319 A218355 A103790

Adjacent sequences:  A053572 A053573 A053574 * A053576 A053577 A053578

KEYWORD

nonn,mult

AUTHOR

Labos Elemer, Jan 18 2000

STATUS

approved

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Last modified December 20 22:23 EST 2014. Contains 252289 sequences.