A230664 -id:A230664 - cp's OEIS frontend

A233441 a(n) = floor(2^n / n^3).

2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 9, 16, 26, 44, 76, 131, 226, 393, 689, 1213, 2147, 3818, 6818, 12228, 22012, 39768, 72084, 131072, 239027, 437102, 801393, 1472896, 2713342, 5009438, 9267786, 17179869, 31906432, 59362467, 110632938, 206519839, 386111079

Offset: 1

Alex Ratushnyak, Dec 09 2013

nonn

Paolo Xausa, Table of n, a(n) for n = 1..1000

Cf. A000079, A000578, A060505, A062278.

Cf. A230664, A233442.

Array[Floor[2^#/#^3] &, 50] (* Paolo Xausa, Mar 27 2025 *)

for n in range(1,100):  print(2**n // n**3, end=', ')

a(n) = floor(A000079(n) / A000578(n)).

A233471 a(n) = 3^n mod n^2.

Original entry on oeis.org

0, 1, 0, 1, 18, 9, 31, 33, 0, 49, 3, 81, 146, 177, 207, 65, 224, 81, 307, 1, 342, 9, 118, 225, 68, 529, 0, 753, 467, 549, 623, 641, 27, 757, 607, 81, 632, 389, 846, 801, 905, 981, 261, 81, 243, 1757, 1554, 2241, 2383, 249, 792, 1329, 851, 729, 1332, 2529, 1737, 2793, 298

Offset: 1

Alex Ratushnyak, Dec 11 2013

			a(4) = 1 because 3^4 = 81, 4^2 = 16 and 81 = 1 mod 80.
a(5) = 18 because 3^5 = 243, 5^2 = 25 and 243 = 18 mod 25.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A000244, A000290, A066606, A066607.

Cf. A233442, A230664.

a:= n-> 3&^n mod n^2:
seq(a(n), n=1..60);  # Alois P. Heinz, Dec 22 2013

Table[Mod[3^n, n^2], {n, 100}] (* Alonso del Arte, Dec 11 2013 *)
Table[PowerMod[3,n,n^2],{n,100}] (* Harvey P. Dale, Aug 27 2019 *)

a(n) = lift(Mod(3, n^2)^n); \\ Michel Marcus, May 05 2021

for n in range(1,100):  print(str(3**n % n**2), end=',')

a(n) = A000244(n) mod A000290(n).

cp's OEIS Frontend

A233441 a(n) = floor(2^n / n^3).

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