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 A226966 Numbers n such that 1^n + 2^n + 3^n + ... + n^n == 8 (mod n). 10
 1, 16, 48, 336, 14448 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also, numbers n such that B(n)*n == 8 (mod n), where B(n) is the n-th Bernoulli number. Equivalently, SUM[prime p, (p-1) divides n] n/p == -8 (mod n). There are no other terms below 10^15. - Max Alekseyev, Aug 26 2013 LINKS Table of n, a(n) for n=1..5. MATHEMATICA Select[Range[10000], Mod[Sum[PowerMod[i, #, #], {i, #}], #] == 8 &] PROG (PARI) is(n)=Mod(sumdiv(n, d, if(isprime(d+1), n/(d+1))), n)==-8 \\ Charles R Greathouse IV, Nov 13 2013 CROSSREFS Cf. A031971. 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), this sequence (m=8), A226967 (m=9), A280041 (m=19), A280043 (m=43), A302343 (m=79), A302344 (m=193). Sequence in context: A223692 A165115 A165117 * A297460 A297697 A231526 Adjacent sequences: A226963 A226964 A226965 * A226967 A226968 A226969 KEYWORD nonn,more AUTHOR José María Grau Ribas, Jun 24 2013 EXTENSIONS a(1)=1 prepended by Max Alekseyev, Aug 26 2013 STATUS approved

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Last modified February 21 12:33 EST 2024. Contains 370235 sequences. (Running on oeis4.)