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Numbers divisible by a square greater than 1 that are the sum of two consecutive numbers divisible by a square greater than 1.
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%I #41 Oct 23 2022 22:53:27

%S 49,99,343,351,775,847,1025,1449,1665,1681,1849,1863,2057,2151,2367,

%T 2575,2825,2889,3175,3185,3249,3609,3625,3699,3725,3751,3871,3951,

%U 4113,4375,4599,4625,4913,5047,5049,5193,5239,5391,5751,5887,6137,6175,6425,6713,6849

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

%C The sequence is infinite as it contains 29400*k + 49 for k >= 0. - _David A. Corneth_, Sep 12 2022

%F A008683(a(n)) = 0.

%e 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.

%t Select[2*Select[Range[5000], ! SquareFreeQ[#] && ! SquareFreeQ[# + 1] &] + 1, ! SquareFreeQ[#] &] (* _Amiram Eldar_, Sep 12 2022 *)

%o (PARI) is(n) = bitand(n, 1) && !issquarefree(n) && !issquarefree(n - n>>1) && !issquarefree(n >> 1) \\ _David A. Corneth_, Sep 12 2022

%Y Subsequence of A013929 and A068781.

%Y Cf. A000290, A008683.

%K nonn

%O 1,1

%A _Daniel Barker_, Sep 12 2022

%E More terms from _Amiram Eldar_, Sep 12 2022