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A229306 Numbers n such that A031971(6*n) <> n (mod 6*n) 16
7, 10, 14, 20, 21, 26, 28, 30, 35, 40, 42, 49, 50, 52, 55, 56, 57, 60, 63, 70, 77, 78, 80, 84, 90, 91, 98, 100, 104, 105, 110, 112, 114, 119, 120, 126, 130, 133, 136, 140, 147, 150, 154, 155, 156, 160, 161, 165, 168, 170, 171, 175, 180, 182, 189, 190, 196 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Complement of A229302.

The asymptotic density is in [0.2927, 0.3014].

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

Table of n, a(n) for n=1..57.

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[6*#] == # &]

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: A191833 A020752 A134302 * A023485 A020721 A015782

Adjacent sequences:  A229303 A229304 A229305 * A229307 A229308 A229309

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Sep 24 2013

STATUS

approved

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Last modified January 27 21:48 EST 2020. Contains 331297 sequences. (Running on oeis4.)