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 A229301 Numbers n such that A031971(42*n) == n (mod 42*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, 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, 82 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Complement of A229305. The asymptotic density is in [0.7880, 0.8079]. 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 Robert Israel, Table of n, a(n) for n = 1..1000 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 MAPLE filter:= proc(n) local t, k;   t:= add(k &^ (42*n) mod (42*n), k=1..42*n);   t mod (42*n) = n end proc: select(filter, [\$1..100]); # Robert Israel, Dec 15 2020 MATHEMATICA g[n_] := Mod[Sum[PowerMod[i, n, n], {i, n}], n]; Select[Range[100], g[42*#] == # &] CROSSREFS Cf. A014117 (numbers n such that A031971(n)==1 (mod 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. 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). Sequence in context: A279367 A020731 A229300 * A277061 A090274 A254621 Adjacent sequences:  A229298 A229299 A229300 * A229302 A229303 A229304 KEYWORD nonn AUTHOR José María Grau Ribas, Sep 21 2013 STATUS approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)