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 A136655 Product of odd divisors of n. 10
 1, 1, 3, 1, 5, 3, 7, 1, 27, 5, 11, 3, 13, 7, 225, 1, 17, 27, 19, 5, 441, 11, 23, 3, 125, 13, 729, 7, 29, 225, 31, 1, 1089, 17, 1225, 27, 37, 19, 1521, 5, 41, 441, 43, 11, 91125, 23, 47, 3, 343, 125, 2601, 13, 53, 729, 3025, 7, 3249, 29, 59, 225, 61, 31, 250047, 1, 4225, 1089 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Product of rows of triangle A182469. - Reinhard Zumkeller, May 01 2012 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(p) = p if p noncomposite; a(2^n) = 1; a(pq) = p^2 * q^2 when p, q are odd primes. a(n) = sqrt(n^od(n)/2^ed(n)), where od(n) = number of odd divisors of n = tau(2*n)-tau(n) and ed(n) = number of even divisors of n = 2*tau(n)-tau(2*n). - Vladeta Jovovic, Jun 25 2008 Also a(n) = A007955(A000265(n)). - David Wilson, Jun 26 2008 a(n) = Product_{h == 1 mod 4 and h | n}*Product_{i == 3 mod 4 and i | n}. a(n) = Product_{j == 1 mod 6 and j | n}*Product_{k == 5 mod 6 and k | n}. a(n) = A140210(n)*A140211(n). - R. J. Mathar, Jun 27 2008 a(n) = A007955(n) / A125911(n). MAPLE with(numtheory); f:=proc(n) local t1, i, k; t1:=divisors(n); k:=1; for i in t1 do if i mod 2 = 1 then k:=k*i; fi; od; k; end; # N. J. A. Sloane, Jul 14 2008 MATHEMATICA Array[Times @@ Select[Divisors@ #, OddQ] &, 66] (* Michael De Vlieger, Aug 03 2017 *) a[n_] := (oddpart = n/2^IntegerExponent[n, 2])^(DivisorSigma[0, oddpart]/2); Array[a, 100] (* Amiram Eldar, Jun 26 2022 *) PROG (Haskell) a136655 = product . a182469_row -- Reinhard Zumkeller, May 01 2012 (PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, if (d[k]%2, d[k], 1)); \\ Michel Marcus, Aug 04 2017 CROSSREFS Cf. A000265, A000593, A007955, A007956, A078701. Cf. A140210, A140211, A140213, A140214, A140215. Cf. A125911, A126192. Cf. A001227, A183063. Sequence in context: A081432 A318060 A336652 * A060819 A318661 A089654 Adjacent sequences: A136652 A136653 A136654 * A136656 A136657 A136658 KEYWORD nonn,easy AUTHOR Jonathan Vos Post, Jun 25 2008 EXTENSIONS More terms from N. J. A. Sloane, Jul 14 2008 Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified March 2 12:27 EST 2024. Contains 370467 sequences. (Running on oeis4.)