A354342 Numbers divisible by a square greater than 1 that are the sum of two consecutive numbers divisible by a square greater than 1.

49, 99, 343, 351, 775, 847, 1025, 1449, 1665, 1681, 1849, 1863, 2057, 2151, 2367, 2575, 2825, 2889, 3175, 3185, 3249, 3609, 3625, 3699, 3725, 3751, 3871, 3951, 4113, 4375, 4599, 4625, 4913, 5047, 5049, 5193, 5239, 5391, 5751, 5887, 6137, 6175, 6425, 6713, 6849

Offset

1,1

Comments

The sequence is infinite as it contains 29400*k + 49 for k >= 0. - David A. Corneth, Sep 12 2022

Links

Table of n, a(n) for n=1..45.

Formula

A008683(a(n)) = 0.

Example

24 is divisible by 2 times 2, 25 by 5 times 5, and 24+25=49 divisible by 7 times 7. Next, 49 is divisible by 7 times 7, 50 is divisible by 5 times 5, the sum is 99 divisible by three times three.

Mathematica

Select[2*Select[Range[5000], ! SquareFreeQ[#] && ! SquareFreeQ[# + 1] &] + 1, ! SquareFreeQ[#] &] (* Amiram Eldar, Sep 12 2022 *)

Prog

(PARI) is(n) = bitand(n, 1) && !issquarefree(n) && !issquarefree(n - n>>1) && !issquarefree(n >> 1) \\ David A. Corneth, Sep 12 2022

Crossrefs

Subsequence of A013929 and A068781.

Cf. A000290, A008683.

Sequence in context: A114013 A235578 A161689 * A230653 A019547 A228878

Adjacent sequences: A354339 A354340 A354341 * A354343 A354344 A354345

Keyword

nonn

Author

Daniel Barker, Sep 12 2022

Extensions

More terms from Amiram Eldar, Sep 12 2022

Status

approved