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 A229300 Numbers n such that A031971(1806*n) == n (mod 1806*n). 17
 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 53, 54, 56, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79, 81 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Complement of A229304. The asymptotic density is in [0.7747,0.812570]. The numbers k = 1, 2, 6, 42, 1806, 47058, 2214502422, 8490421583559688410706771261086 = A230311 are the only values of k such that the set {n: A031971(k*n) == n (mod k*n)} is nonempty. Its smallest element is n = 1, 1, 1, 1, 1, 5, 5, 39607528021345872635 = A231409. (Comment corrected and expanded by Jonathan Sondow, Dec 10 2013.) LINKS Jose María Grau, A. M. Oller-Marcen, and J. Sondow, On the congruence 1^n + 2^n +... + n^n = d (mod n), where d divides n MATHEMATICA g[n_] := Mod[Sum[PowerMod[i, n, n], {i, n}], n]; Select[Range[100], g[1806*#] == # &] CROSSREFS Cf. A031971, A231409. Cf. A231562 (numbers n such that A031971(8490421583559688410706771261086*n) == n (mod 8490421583559688410706771261086*n)). Cf. A229312 (numbers n such that A031971(47058*n) == n (mod 47058*n)). Cf. A229300 (numbers n such that A031971(1806*n)== n (mod n*1806)). Cf. A229301 (numbers n such that A031971(42*n) == n (mod 42*n)). Cf. A229302 (numbers n such that A031971(6*n) == n (mod 6*n)). Cf. A229303 (numbers n such that A031971(2*n) == n (mod 2*n)). Cf. A229313 (numbers n such that A031971(47058*n) <> n (mod 47058*n)). Cf. A229304 (numbers n such that A031971(1806*n) <> n (mod n*1806)). Cf. A229305 (numbers n such that A031971(42*n) <> n (mod 42*n)). Cf. A229306 (numbers n such that A031971(6*n) <> n (mod 6*n)). Cf. A229307 (numbers n such that A031971(2*n) <> n (mod 2*n)). Cf. A229308 (primitive numbers in A229304). Cf. A229309 (primitive numbers in A229305). Cf. A229310 (primitive numbers in A229306). Cf. A229311 (primitive numbers in A229307). Cf. A054377 (primary pseudoperfect numbers). Sequence in context: A069570 A279367 A020731 * A229301 A277061 A090274 Adjacent sequences:  A229297 A229298 A229299 * A229301 A229302 A229303 KEYWORD nonn AUTHOR José María Grau Ribas, Sep 19 2013 STATUS approved

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Last modified May 21 06:36 EDT 2022. Contains 353889 sequences. (Running on oeis4.)