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 A061142 Replace each prime factor of n with 2: a(n) = 2^bigomega(n), where bigomega = A001222, number of prime factors counted with multiplicity. 27
 1, 2, 2, 4, 2, 4, 2, 8, 4, 4, 2, 8, 2, 4, 4, 16, 2, 8, 2, 8, 4, 4, 2, 16, 4, 4, 8, 8, 2, 8, 2, 32, 4, 4, 4, 16, 2, 4, 4, 16, 2, 8, 2, 8, 8, 4, 2, 32, 4, 8, 4, 8, 2, 16, 4, 16, 4, 4, 2, 16, 2, 4, 8, 64, 4, 8, 2, 8, 4, 8, 2, 32, 2, 4, 8, 8, 4, 8, 2, 32, 16, 4, 2, 16, 4, 4, 4, 16, 2, 16, 4, 8, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The inverse Möbius transform of A162510. - R. J. Mathar, Feb 09 2011 LINKS R. Zumkeller, Table of n, a(n) for n = 1..10000 R. J. Mathar, Survey of Dirichlet Series of Multiplicative Arithmetic Functions, arXiv:1106.4038 [math.NT], 2011-2012. See eq. (2.12). FORMULA a(n) = Sum_{d divides n} 2^(bigomega(d)-omega(d)) = Sum_{d divides n} 2^(A001222(d) - A001221(d)). - Benoit Cloitre, Apr 30 2002 a(n) = A000079(A001222(n)), i.e., a(n)=2^bigomega(n). - Emeric Deutsch, Feb 13 2005 Totally multiplicative with a(p) = 2. - Franklin T. Adams-Watters, Oct 04 2006 Dirichlet g.f.: Product_{p prime} 1/(1-2*p^(-s)). - Ralf Stephan, Mar 28 2015 a(n) = A001316(A156552(n)). - Antti Karttunen, May 29 2017 EXAMPLE a(100)=16 since 100=2*2*5*5 and so a(100)=2*2*2*2. MAPLE with(numtheory): seq(2^bigomega(n), n=1..95); MATHEMATICA Table[2^PrimeOmega[n], {n, 1, 95}] (* Jean-François Alcover, Jun 08 2013 *) PROG (PARI) a(n)=direuler(p=1, n, 1/(1-2*X))[n] /* Ralf Stephan, Mar 28 2015 */ (PARI) a(n) = 2^bigomega(n); \\ Michel Marcus, Aug 08 2017 CROSSREFS Cf. A000079, A001222, A001316, A034444, A123667, A124508, A156552. Sequence in context: A085191 A188581 A165872 * A278525 A226083 A182730 Adjacent sequences:  A061139 A061140 A061141 * A061143 A061144 A061145 KEYWORD easy,nonn,mult AUTHOR Henry Bottomley, May 29 2001 STATUS approved

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