cp's OEIS Frontend

A145737 a(n) = square part of A145609(n).

%I A145737 #18 Feb 27 2024 07:36:16
%S A145737 1,5,7,1,11,13,1,17,19,1,23,1,1,29,31,1,1,37,1,41,43,1,47,1,1,53,1,1,
%T A145737 59,61,1,1,67,1,71,73,1,1,79,1,83,1,1,89,1,1,1,97,1,101,103,1,107,109,
%U A145737 1,113,1,1,1,1,1,1,127,1,131,1,1,137,139,1,1,1,1,149,151,1,1,157,1,1,163
%N A145737 a(n) = square part of A145609(n).
%C A145737 For squarefree parts see A145738. A128059 is a very similar sequence.
%F A145737 a(n) = 2n+1 if 2n+1 is prime, 1 otherwise, for n > 1.
%F A145737 From _Gary Detlefs_, Oct 18 2011: (Start)
%F A145737 a(n) = Denominator(n!*(Sum_{k=1..n} k^3)/(Sum_{k=1..n} k^2))
%F A145737      = Denominator(n!*3*n*(n+1)/(2*(2*n+1))). (End)
%p A145737 seq(denom(n!*3*n*(n+1)/(2*(2*n+1))), n=1..81); # _Gary Detlefs_, Oct 18 2011
%t A145737 m = 1; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; b = Sqrt[Numerator[k]] /. Sqrt[_] -> 1; AppendTo[aa, b], {r, 1, 137}]; aa (* _Artur Jasinski_ *)
%o A145737 (Python)
%o A145737 from sympy import isprime
%o A145737 def A145737(n): return a if isprime(a:=(n<<1)+1) and n>1 else 1 # _Chai Wah Wu_, Feb 26 2024
%Y A145737 Cf. A008833, A128059, A145609, A145738.
%K A145737 nonn
%O A145737 1,2
%A A145737 _Artur Jasinski_, Oct 17 2008