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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
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
Sequence in context: A081432 A318060 A336652 * A060819 A318661 A089654
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.)