This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A136655 #36 Jun 27 2025 20:59:37
%S A136655 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,
%T A136655 729,7,29,225,31,1,1089,17,1225,27,37,19,1521,5,41,441,43,11,91125,23,
%U A136655 47,3,343,125,2601,13,53,729,3025,7,3249,29,59,225,61,31,250047,1,4225,1089
%N A136655 Product of odd divisors of n.
%C A136655 Product of rows of triangle A182469. - _Reinhard Zumkeller_, May 01 2012
%H A136655 Reinhard Zumkeller, <a href="/A136655/b136655.txt">Table of n, a(n) for n = 1..10000</a>
%F A136655 a(p) = p if p noncomposite; a(2^n) = 1; a(pq) = p^2 * q^2 when p, q are odd primes.
%F A136655 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
%F A136655 Also a(n) = A007955(A000265(n)). - David Wilson, Jun 26 2008
%F A136655 a(n) = Product_{h == 1 mod 4 and h | n}*Product_{i == 3 mod 4 and i | n}.
%F A136655 a(n) = Product_{j == 1 mod 6 and j | n}*Product_{k == 5 mod 6 and k | n}.
%F A136655 a(n) = A140210(n)*A140211(n). - _R. J. Mathar_, Jun 27 2008
%F A136655 a(n) = A007955(n) / A125911(n).
%p A136655 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
%t A136655 Array[Times @@ Select[Divisors@ #, OddQ] &, 66] (* _Michael De Vlieger_, Aug 03 2017 *)
%t A136655 a[n_] := (oddpart = n/2^IntegerExponent[n, 2])^(DivisorSigma[0, oddpart]/2); Array[a, 100] (* _Amiram Eldar_, Jun 26 2022 *)
%o A136655 (Haskell)
%o A136655 a136655 = product . a182469_row -- _Reinhard Zumkeller_, May 01 2012
%o A136655 (PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, if (d[k]%2, d[k], 1)); \\ _Michel Marcus_, Aug 04 2017
%o A136655 (Python)
%o A136655 from math import isqrt
%o A136655 from sympy import divisor_count
%o A136655 def A136655(n):
%o A136655 d = divisor_count(m:=n>>(~n&n-1).bit_length())
%o A136655 return isqrt(m)**d if d&1 else m**(d>>1) # _Chai Wah Wu_, Jun 27 2025
%Y A136655 Cf. A000265, A000593, A007955, A007956, A078701.
%Y A136655 Cf. A140210, A140211, A140213, A140214, A140215.
%Y A136655 Cf. A125911, A126192.
%Y A136655 Cf. A001227, A183063.
%K A136655 nonn,easy
%O A136655 1,3
%A A136655 _Jonathan Vos Post_, Jun 25 2008
%E A136655 More terms from _N. J. A. Sloane_, Jul 14 2008
%E A136655 Edited by _N. J. A. Sloane_, Aug 29 2008 at the suggestion of _R. J. Mathar_