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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. 48
 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..10005 R. J. Mathar, Survey of Dirichlet Series of Multiplicative Arithmetic Functions, arXiv:1106.4038 [math.NT], 2011-2012. See eq. (2.12). Index entries for sequences computed from exponents in factorization of n 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 Dirichlet g.f.: zeta(s)^2 * Product_{p prime} 1/(1 - 1/(p^s - 1)^2). - Vaclav Kotesovec, Mar 14 2023 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, A069205 (partial sums), A123667, A124508, A156552. Sequence in context: A318316 A328721 A165872 * A318312 A318474 A326306 Adjacent sequences: A061139 A061140 A061141 * A061143 A061144 A061145 KEYWORD easy,nonn,mult AUTHOR Henry Bottomley, May 29 2001 STATUS approved

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Last modified May 23 22:02 EDT 2024. Contains 372765 sequences. (Running on oeis4.)