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

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, 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, 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

Offset: 1

Author

Artur Jasinski, Oct 17 2008

Keywords

• nonn

Comments

For squarefree parts see A145738. A128059 is a very similar sequence.

Crossrefs

Cf. A008833, A128059, A145609, A145738.

Programs

Maple

seq(denom(n!*3*n*(n+1)/(2*(2*n+1))), n=1..81); # Gary Detlefs, Oct 18 2011

Mathematica

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 *)

Python

from sympy import isprime
def A145737(n): return a if isprime(a:=(n<<1)+1) and n>1 else 1 # Chai Wah Wu, Feb 26 2024

Formula

a(n) = 2n+1 if 2n+1 is prime, 1 otherwise, for n > 1.

From Gary Detlefs, Oct 18 2011: (Start)

a(n) = Denominator(n!*(Sum_{k=1..n} k^3)/(Sum_{k=1..n} k^2))

= Denominator(n!*3*n*(n+1)/(2*(2*n+1))). (End)