A341890 -id:A341890 - cp's OEIS frontend

A341889 a(n) is the smallest positive integer k > 1 such that n + k divides n^n + k, or 0 if no such k exists.

2, 0, 3, 2, 3, 4, 2, 6, 3, 5, 4, 10, 2, 12, 5, 2, 3, 16, 2, 18, 3, 4, 10, 22, 3, 24, 9, 8, 6, 28, 2, 30, 7, 17, 5, 6, 2, 36, 9, 5, 3, 40, 6, 42, 3, 4, 22, 46, 2, 20, 4, 16, 7, 52, 2, 14, 3, 5, 28, 58, 2, 60, 9, 8, 3, 9, 2, 66, 11, 20, 4, 70, 3, 72, 20, 14, 3, 8, 5, 78, 4, 32, 40, 82, 2, 24, 29, 11, 3, 88, 2, 6, 7, 23

Offset: 1

Seiichi Manyama, Jun 04 2021

nonn

k > 1 is needed in the definition as n+1 divides n^n+1 for all odd n. - Chai Wah Wu, Jun 04 2021

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A242789, A242801, A242899, A301941, A341760, A341844, A341890, A341902.

a[n_] := Module[{k = 2}, While[! Divisible[n^n + k, n + k], k++]; k]; Array[a, 100, 3] (* Amiram Eldar, Jun 04 2021 *)

a(n) = if(n==2, 0, my(k=2); while((n^n+k)%(n+k)!=0, k++); k);

A341760 Least k > 1 such that (n^k+k)/(n+k) is an integer.

Original entry on oeis.org

2, 2, 7, 3, 2, 3, 4, 5, 5, 3, 5, 5, 7, 11, 7, 5, 4, 7, 16, 5, 15, 3, 4, 9, 22, 5, 13, 6, 8, 7, 19, 7, 9, 11, 5, 5, 6, 19, 13, 9, 12, 7, 9, 5, 11, 10, 23, 5, 4, 7, 7, 9, 13, 19, 21, 5, 7, 13, 29, 9, 5, 4, 19, 9, 8, 7, 12, 10, 17, 7, 17, 6, 13, 5, 31, 5, 9, 7, 8, 7, 25, 9, 41, 15, 21, 10, 19, 9, 28, 11, 15

Offset: 0

Seiichi Manyama, Jun 04 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A242801, A242899, A341844, A341889, A341890.

a[n_] := Module[{k = 2}, While[! Divisible[n^k + k, n + k], k++]; k]; Array[a, 100, 0] (* Amiram Eldar, Jun 04 2021 *)

a(n) = my(k=2); while((n^k+k)%(n+k)!=0, k++); k;

A341844 Least k > 1 such that (n+k^n)/(n+k) is an integer.

Original entry on oeis.org

2, 4, 3, 6, 3, 5, 2, 4, 3, 3, 4, 14, 2, 7, 5, 18, 3, 20, 2, 8, 3, 7, 10, 6, 3, 13, 9, 9, 6, 29, 2, 12, 7, 12, 5, 38, 2, 19, 9, 13, 3, 41, 6, 11, 3, 15, 22, 8, 2, 25, 4, 39, 7, 12, 2, 13, 3, 60, 28, 62, 2, 31, 9, 10, 3, 5, 2, 24, 11, 24, 4, 74, 3, 37, 20, 25, 3, 80, 5, 10, 4, 9, 40, 18, 2, 37, 29, 16, 3, 15, 2

Offset: 1

Seiichi Manyama, Jun 04 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A242801, A242899, A341760, A341889, A341890.

a[n_] := Module[{k = 2}, While[! Divisible[k^n + n, n + k], k++]; k]; Array[a, 100] (* Amiram Eldar, Jun 04 2021 *)

a(n) = my(k=2); while((n+k^n)%(n+k)!=0, k++); k;

cp's OEIS Frontend

A341889 a(n) is the smallest positive integer k > 1 such that n + k divides n^n + k, or 0 if no such k exists.

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A341760 Least k > 1 such that (n^k+k)/(n+k) is an integer.

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A341844 Least k > 1 such that (n+k^n)/(n+k) is an integer.

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