A231563 -id:A231563 - cp's OEIS frontend

A231564 Numbers such that A231563(n)=0.

1, 3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88

Offset: 1

José María Grau Ribas, Dec 09 2013

nonn

This sequence contains the odd primes.

Cf. A231563, A231565.

S[n_] := Mod[Sum[If[GCD[i, n] == 1, PowerMod[i, n, n], 0], {i, 1, n}], n];Select[Range[100],S[#]==0&]

A231565 Numbers such that A231563(n)>0.

Original entry on oeis.org

2, 4, 6, 8, 12, 16, 18, 20, 24, 30, 32, 36, 40, 42, 48, 54, 60, 64, 66, 72, 80, 84, 90, 96, 100, 102, 108, 110, 120, 126, 128, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 180, 192, 198, 200, 204, 210, 216, 220, 240, 246, 252, 256, 260, 264, 270, 272

Offset: 1

José María Grau Ribas, Dec 09 2013

nonn

Cf. A231563, A231564.

S[n_] := Mod[Sum[If[GCD[i, n] == 1, PowerMod[i, n, n], 0], {i, 1, n}], n]; Select[Range[1200], ! S[#] == 0 &]

A263014 a(n) = Sum_{0 < a, b <= n and gcd(a^2 + b^2, n) = 1} (a + bi)^n (mod n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0

Offset: 1

José María Grau Ribas, Oct 07 2015

nonn

Sum of the n-th powers of the invertible elements of Z[i]/nZ[i].

Hans Havermann, Table of n, a(n) for n = 1..5000

See A263016 for indices where this is nonzero.
See A290287 for the nonzero values.
Cf. A231563, A231564, A231565.

Sp[n_, k_] := Mod[Sum[If[GCD[a^2 + b^2, n] == 1, PowerMod[(a + b I), k, n], 0], {a, n}, {b, n}], n]; Table[ Sp[n, n] , {n, 1, 74}]

A231566 gcd(1,2n)1^2n + ...+ gcd(i,2n)i^2n + ... + gcd(2n,2n)*2n^2n (mod 2n).

Original entry on oeis.org

1, 2, 3, 4, 5, 10, 7, 8, 9, 2, 11, 4, 13, 14, 15, 16, 17, 30, 19, 20, 27, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 12, 37, 38, 39, 72, 41, 58, 43, 44, 45, 46, 47, 80, 49, 10, 51, 52, 53, 90, 105, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67

Offset: 1

José María Grau Ribas, Dec 09 2013

nonn

Gf. A231563, A231567.

Su[n_] := Su[n] = Mod[Sum[GCD[i, n]*PowerMod[i, n, n], {i, 1, n}], n];Table[Su[2n],{n,1,44}]

cp's OEIS Frontend

A231564 Numbers such that A231563(n)=0.

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A231565 Numbers such that A231563(n)>0.

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A263014 a(n) = Sum_{0 < a, b <= n and gcd(a^2 + b^2, n) = 1} (a + bi)^n (mod n).

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A231566 gcd(1,2n)1^2n + ...+ gcd(i,2n)i^2n + ... + gcd(2n,2n)*2n^2n (mod 2n).

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cp's OEIS Frontend

A231564 Numbers such that A231563(n)=0.

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Author

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A231565 Numbers such that A231563(n)>0.

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Author

Keywords

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Mathematica

A263014 a(n) = Sum_{0 < a, b <= n and gcd(a^2 + b^2, n) = 1} (a + bi)^n (mod n).

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Author

Keywords

Comments

Links

Crossrefs

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Mathematica

A231566 gcd(1,2n)*1^2n + ...+ gcd(i,2n)*i^2n + ... + gcd(2n,2n)*2n^2n (mod 2n).

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Author

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Crossrefs

Programs

Mathematica

A231566 gcd(1,2n)1^2n + ...+ gcd(i,2n)i^2n + ... + gcd(2n,2n)*2n^2n (mod 2n).