A305211 -id:A305211 - cp's OEIS frontend

A305212 a(n) = n - A305211(n).

0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 6, 0, 0, 0, 0, 0, 12, 8, 0, 0, 0, 0, 0, 0, 10, 16, 0, 0, 0, 0, 0, 12, 0, 0, 20, 0, 0, 0, 14, 0, 0, 0, 0, 24, 0, 16, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 20, 0, 32, 0, 0, 0, 0, 22, 0, 0, 0, 36, 0, 0

Offset: 1

Jack Zhang, May 27 2018

nonn

Number of integers d from 0 to n-1 such that x^3 + y^3 == d (mod n) has no solutions in integers.

Cf. A305211.

a(n) = my(v=[]); for (x=1, n, for (y=1, n, v = concat(v, Mod(x, n)^3 + Mod(y, n)^3))); n - #Set(v); \\ Michel Marcus, Jul 10 2018

[n-len(set((pow(x,3,n)+pow(y,3,n))%n for x in range(n) for y in range(x+1))) for n in range(1,51)]

a(50)-a(83) from Jon E. Schoenfield, May 28 2018

A305214 Numbers k such that A305212(k) is not zero.

Original entry on oeis.org

7, 9, 14, 18, 21, 27, 28, 35, 36, 42, 45, 49, 54, 56, 63, 70, 72, 77, 81, 84, 90, 91, 98, 99, 105, 108, 112, 117, 119, 126, 133, 135, 140, 144, 147, 153, 154, 161, 162, 168, 171, 175, 180, 182, 189, 196, 198, 203, 207, 210, 216, 217, 224, 225, 231, 234, 238

Offset: 1

Jack Zhang, May 27 2018

nonn

Conjecture: These are simply the positive integers that are divisible by 7 or 9.

Cf. A305211, A305212.

isok(n) = my(v=[]); for (x=1, n, for (y=1, n, v = concat(v, Mod(x, n)^3 + Mod(y, n)^3))); n != #Set(v); \\ Michel Marcus, Jul 10 2018

[n for n in range(100) if n != len(set((pow(x,3,n) + pow(y,3,n))%n for x in range(n) for y in range(n)))]

a(25)-a(57) from Jon E. Schoenfield, May 28 2018

cp's OEIS Frontend

A305212 a(n) = n - A305211(n).

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