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 A162510 Dirichlet inverse of A076479. 6
 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 1, 8, 1, 2, 1, 2, 1, 1, 1, 4, 2, 1, 4, 2, 1, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 8, 2, 2, 1, 2, 1, 4, 1, 4, 1, 1, 1, 2, 1, 1, 2, 32, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 2, 2, 1, 1, 1, 8, 8, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 16, 1, 2, 2, 4, 1, 1, 1, 4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Apart from signs, this sequence is identical to A162512. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 G. P. Michon, Multiplicative functions FORMULA Multiplicative with a(p^e) = 2^(e-1) for any prime p and any positive exponent e. a(n) = n/2 when n is a power of 2 (A000079). a(n) = 1 when n is a squarefree number (A005117). a(n) = 2^A046660(n) = A061142(n)/A034444(n). - R. J. Mathar, Nov 02 2016 MAPLE A162510 := proc(n)     local a, f;     a := 1;     for f in ifactors(n)[2] do         a := a*2^(op(2, f)-1) ;     end do:     return a; end proc: # R. J. Mathar, May 20 2017 MATHEMATICA a[n_] := 2^(PrimeOmega[n] - PrimeNu[n]); Array[a, 100] (* Jean-François Alcover, Apr 24 2017, after R. J. Mathar *) PROG (PARI) a(n)=my(f=factor(n)[, 2]); 2^(vecsum(f)-#f) \\ Charles R Greathouse IV, Nov 02 2016 (Python) from sympy import factorint from operator import mul def a(n):     f=factorint(n)     return 1 if n==1 else reduce(mul, [2**(f[i] - 1) for i in f]) # Indranil Ghosh, May 20 2017 CROSSREFS Cf. A076479, A162511, A162512. Sequence in context: A173398 A104404 A162512 * A235388 A252733 A181876 Adjacent sequences:  A162507 A162508 A162509 * A162511 A162512 A162513 KEYWORD easy,mult,nonn,changed AUTHOR Gerard P. Michon, Jul 05 2009 STATUS approved

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