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 A229305 Numbers n such that A031971(42*n) <> n (mod 42*n). 16
 10, 20, 26, 30, 40, 43, 50, 52, 55, 57, 58, 60, 70, 78, 80, 86, 90, 100, 104, 110, 114, 116, 120, 129, 130, 136, 140, 150, 155, 156, 160, 165, 170, 171, 172, 174, 180, 182, 190, 200, 208, 210, 215, 220, 222, 228, 230, 232, 234, 240, 250, 253, 258, 260, 270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Complement of A229301. The asymptotic density is in [0.2091, 0.2317]. If n is in A then k*n is in A for all natural number k. 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[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: A179819 A320522 A072592 * A229304 A101869 A015872 Adjacent sequences:  A229302 A229303 A229304 * A229306 A229307 A229308 KEYWORD nonn AUTHOR José María Grau Ribas, Sep 23 2013 STATUS approved

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Last modified November 27 16:20 EST 2021. Contains 349394 sequences. (Running on oeis4.)