A324178 -id:A324178 - cp's OEIS frontend

A324177 Integers k such that floor(sqrt(k)) + floor(sqrt(k/4)) divides k.

1, 2, 3, 6, 12, 18, 24, 28, 35, 36, 45, 50, 60, 72, 91, 105, 120, 128, 144, 162, 171, 190, 210, 242, 264, 288, 300, 324, 351, 364, 392, 420, 465, 495, 528, 544, 576, 612, 629, 666, 702, 760, 798, 840, 860, 900, 945, 966, 1012, 1056, 1127, 1173, 1224, 1248, 1296

Offset: 1

Jinyuan Wang, Mar 09 2019

nonn

k = 36*j^2 is a term for j > 0.

Other infinite families of terms are 36*j^2-29*j+5, 36*j^2-21*j+3, 36*j^2-12*j, 36*j^2-8*j,36*j^2+9*j,36*j^2+13*j+1,36*j^2+22*j+2, and 36*j^2+30*j+6. These cover all terms <= 4676406 except 35. - Robert Israel, Jan 24 2020

Robert Israel, Table of n, a(n) for n = 1..3200

Cf. A324174, A324175, A324176, A324178.

filter:= n -> n mod (floor(sqrt(n))+floor(sqrt(n/4))) = 0:
select(filter, [$1..10000]); # Robert Israel, Jan 24 2020

Select[Range[1296], Mod[#, Floor@ Sqrt@ # + Floor@ Sqrt[#/4]] == 0 &] (* Giovanni Resta, Apr 05 2019 *)

is(n) = n%(floor(sqrt(n)) + floor(sqrt(n/4))) == 0;

A324174 Integers k such that 2*floor(sqrt(k)) divides k.

Original entry on oeis.org

2, 4, 8, 12, 16, 24, 30, 36, 48, 56, 64, 80, 90, 100, 120, 132, 144, 168, 182, 196, 224, 240, 256, 288, 306, 324, 360, 380, 400, 440, 462, 484, 528, 552, 576, 624, 650, 676, 728, 756, 784, 840, 870, 900, 960, 992, 1024, 1088, 1122, 1156, 1224, 1260, 1296

Offset: 1

Jinyuan Wang, Mar 09 2019

nonn

Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Cf. A006446, A324175, A324176, A324177, A324178.

Select[ Range[ 1000 ], Mod[ #, 2*Floor[ Sqrt[ # ]//N ] ]==0& ]
LinearRecurrence[{1,0,2,-2,0,-1,1},{2,4,8,12,16,24,30},70] (* Harvey P. Dale, Dec 11 2022 *)

PARI
```
is(n) = n%(2*sqrtint(n)) == 0;
```

For k >= 1, a(3k-2) = 4k^2 - 2k, a(3k-1) = 4k^2 and a(3k) = 4k^2 + 4k.

cp's OEIS Frontend

A324177 Integers k such that floor(sqrt(k)) + floor(sqrt(k/4)) divides k.

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