A121628 -id:A121628 - cp's OEIS frontend

A287335 Nonnegative numbers k such that 3*k + 2 is a cube.

2, 41, 170, 443, 914, 1637, 2666, 4055, 5858, 8129, 10922, 14291, 18290, 22973, 28394, 34607, 41666, 49625, 58538, 68459, 79442, 91541, 104810, 119303, 135074, 152177, 170666, 190595, 212018, 234989, 259562, 285791, 313730, 343433, 374954, 408347, 443666, 480965

Offset: 1

Bruno Berselli, May 23 2017

Corresponding cubes are listed in A016791.

Primes in the sequence: 2, 41, 443, 1637, 22973, 34607, 91541, 234989, ...

Bruno Berselli, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Subsequence of A047292.
Cf. A016791, A131476, A212069.
Cf. A244728: nonnegative k such that 3*k is a cube.
Cf. A121628: nonnegative k such that 3*k + 1 is a cube.

Magma
```
[9*n^3-9*n^2+3*n-1: n in [1..40]];
```

Table[9 n^3 - 9 n^2 + 3 n - 1, {n, 0, 40}]
LinearRecurrence[{4,-6,4,-1},{2,41,170,443},40] (* Harvey P. Dale, Aug 28 2021 *)

Maxima
```
makelist(9*n^3-9*n^2+3*n-1, n, 1, 40);
```

[9*n**3-9*n**2+3*n-1 for n in range(1,40)]

Sage
```
[9*n^3-9*n^2+3*n-1 for n in (1..40)]
```

O.g.f.: x*(2 + 33*x + 18*x^2 + x^3)/(1 - x)^4.
E.g.f.: 1 - (1 - 3*x - 18*x^2 - 9*x^3)*exp(x).
a(n) = 9*n^3 - 9*n^2 + 3*n - 1.
a(n) = A131476(3*n-1) = A212069(3*n-1).

A268861 Cubefree numbers n such that n + 1 is a perfect cube.

Original entry on oeis.org

7, 26, 63, 124, 215, 342, 511, 1330, 1727, 2196, 2743, 3374, 4095, 7999, 9260, 10647, 12166, 13823, 17575, 19682, 24388, 26999, 29790, 32767, 39303, 42874, 46655, 54871, 59318, 63999, 74087, 79506, 85183, 91124, 103822, 110591, 124999, 132650, 140607, 148876

Offset: 1

K. D. Bajpai, Feb 14 2016

nonn

Intersection of A004709 and A068601. - Michel Marcus, Feb 15 2016

			a(2) = 26 = 2 * 13 that is cubefree. 26 + 1 = 27 = 3^3 (perfect cube).
a(4) = 124 = 2 * 2 * 31 that is cubefree. 124 + 1 = 125 = 5^3 (perfect cube).

K. D. Bajpai, Table of n, a(n) for n = 1..400

Cf. A004709, A068601, A121628, A221793, A268752.

cubefree:= proc(n) local t;
  max(seq(t[2],t=ifactors(n)[2])) <= 2
end proc:
select(cubefree, [seq(i^3-1,i=2..100)]); # Robert Israel, Mar 03 2016

Select[Range[150000], FreeQ[FactorInteger[#], {, k /; k > 2}] && IntegerQ[CubeRoot[# + 1]] &]
Select[Range[2,70]^3,Max[FactorInteger[#-1][[All,2]]]<3&]-1 (* Harvey P. Dale, Oct 11 2021 *)

for(n=1, 1e5, f = factor(n)[, 2]; if((#f == 0) || vecmax(f) < 3, if(ispower(n + 1, 3), print1(n, ", "))));

cp's OEIS Frontend

A287335 Nonnegative numbers k such that 3*k + 2 is a cube.

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