A302344 Solutions to the congruence 1^n + 2^n + ... + n^n == 193 (mod n).

1, 2, 6, 193, 386, 1158, 8106, 348558

Offset

1,2

Comments

Also, integers n such that B(n)*n == 193 (mod n), where B(n) is the n-th Bernoulli number.

Also, integers n such that Sum_{prime p, (p-1) divides n} n/p == -193 (mod n).

Although this sequence is finite, the prime 193 does not belong to A302345.

Links

Table of n, a(n) for n=1..8.

M. A. Alekseyev, J. M. Grau, A. M. Oller-Marcen. Computing solutions to the congruence 1^n + 2^n + ... + n^n == p (mod n). Discrete Applied Mathematics, 2018. doi:10.1016/j.dam.2018.05.022 arXiv:1602.02407 [math.NT]

Crossrefs

Solutions to 1^n+2^n+...+n^n == m (mod n): A005408 (m=0), A014117 (m=1), A226960 (m=2), A226961 (m=3), A226962 (m=4), A226963 (m=5), A226964 (m=6), A226965 (m=7), A226966 (m=8), A226967 (m=9), A280041 (m=19), A280043 (m=43), A302343 (m=79), this sequence (m=193).

Cf. A302345.

Sequence in context: A055696 A158096 A345726 * A156517 A333944 A091439

Adjacent sequences: A302341 A302342 A302343 * A302345 A302346 A302347

Keyword

nonn,fini,full

Author

Max Alekseyev, Apr 05 2018

Status

approved