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 A344337 a(n) = 9^omega(n), where omega(n) is the number of distinct primes dividing n. 1
 1, 9, 9, 9, 9, 81, 9, 9, 9, 81, 9, 81, 9, 81, 81, 9, 9, 81, 9, 81, 81, 81, 9, 81, 9, 81, 9, 81, 9, 729, 9, 9, 81, 81, 81, 81, 9, 81, 81, 81, 9, 729, 9, 81, 81, 81, 9, 81, 9, 81, 81, 81, 9, 81, 81, 81, 81, 81, 9, 729, 9, 81, 81, 9, 81, 729, 9, 81, 81, 729, 9, 81, 9, 81, 81, 81 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..76. FORMULA a(n) = A001019(A001221(n)). Multiplicative with a(p^e) = 9. a(n) = Sum_{d|n} mu(d)^2 * tau(d)^3. Dirichlet g.f.: Product_{p prime} (1 + 9/(p^s-1)). - Amiram Eldar, Sep 19 2023 MATHEMATICA Table[9^PrimeNu[n], {n, 1, 100}] (* Amiram Eldar, May 15 2021 *) PROG (PARI) a(n) = 9^omega(n); (PARI) a(n) = prod(k=1, #f=factor(n)[, 2], 9); (PARI) a(n) = sumdiv(n, d, moebius(d)^2*numdiv(d)^3); CROSSREFS k^omega(n): A034444 (k=2), A074816 (k=3), A082476 (k=5), this sequence (k=9). Cf. A000005, A001019, A001221. Sequence in context: A242893 A275485 A346263 * A293832 A277223 A144586 Adjacent sequences: A344334 A344335 A344336 * A344338 A344339 A344340 KEYWORD nonn,mult AUTHOR Seiichi Manyama, May 15 2021 STATUS approved

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Last modified September 11 02:28 EDT 2024. Contains 375813 sequences. (Running on oeis4.)