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

1,2

Comments

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

Links

Table of n, a(n) for n=1..81.

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)

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 *)

Prog

(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

Crossrefs

Cf. A008833, A128059, A145609, A145738.

Sequence in context: A232811 A316132 A261159 * A108763 A061415 A196847

Adjacent sequences: A145734 A145735 A145736 * A145738 A145739 A145740

Keyword

nonn

Author

Artur Jasinski, Oct 17 2008

Status

approved