login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 *)

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: A162742 A081432 A318060 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 15 13:52 EDT 2018. Contains 316236 sequences. (Running on oeis4.)