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A003958
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If n = Product p(k)^e(k) then a(n) = Product (p(k)-1)^e(k), a(1) = 1.
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32
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1, 1, 2, 1, 4, 2, 6, 1, 4, 4, 10, 2, 12, 6, 8, 1, 16, 4, 18, 4, 12, 10, 22, 2, 16, 12, 8, 6, 28, 8, 30, 1, 20, 16, 24, 4, 36, 18, 24, 4, 40, 12, 42, 10, 16, 22, 46, 2, 36, 16, 32, 12, 52, 8, 40, 6, 36, 28, 58, 8, 60, 30, 24, 1, 48, 20, 66, 16, 44, 24, 70, 4, 72, 36, 32, 18, 60, 24, 78, 4, 16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Completely multiplicative.
a(n) = A000010(n) iff n is squarefree (see A005117). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 05 2004
Dirichlet inverse of A097945. - R. J. Mathar, Aug 29 2011
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LINKS
| Daniel Forgues, Table of n, a(n) for n=1..100000
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FORMULA
| Multiplicative with a(p^e) = (p-1)^e. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01 2001.
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MATHEMATICA
| DirichletInverse[f_][1] = 1/f[1]; DirichletInverse[f_][n_] := DirichletInverse[f][n] = -1/f[1]*Sum[ f[n/d]*DirichletInverse[f][d], {d, Most[ Divisors[n]]}]; muphi[n_] := MoebiusMu[n]*EulerPhi[n]; Table[ DirichletInverse[ muphi][n], {n, 1, 81}] (* From Jean-François Alcover, Dec 12 2011, after R. J. Mathar *)
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PROG
| (PARI) a(n)=if(n<1, 0, direuler(p=2, n, 1/(1-p*X+X))[n]) (from R. Stephan)
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CROSSREFS
| Cf. A003959.
Cf. A168065, A168066. [From Daniel Forgues (squid(AT)zensearch.com), Dec 01 2009]
Sequence in context: A187203 A187202 A125131 * A082729 A175542 A076686
Adjacent sequences: A003955 A003956 A003957 * A003959 A003960 A003961
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KEYWORD
| nonn,mult,nice
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AUTHOR
| Marc LeBrun (mlb(AT)well.com)
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EXTENSIONS
| Definition reedited (from formula) by Daniel Forgues (squid(AT)zensearch.com), Nov 17 2009
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