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A229307
Numbers k such that A031971(2*k) <> k (mod 2*k).
19
3, 6, 9, 10, 12, 15, 18, 20, 21, 24, 27, 30, 33, 36, 39, 40, 42, 45, 48, 50, 51, 54, 55, 57, 60, 63, 66, 69, 70, 72, 75, 78, 80, 81, 84, 87, 90, 93, 96, 99, 100, 102, 105, 108, 110, 111, 114, 117, 120, 123, 126, 129, 130, 132, 135, 136, 138, 140, 141, 144
OFFSET
1,1
COMMENTS
Complement of A229303.
The asymptotic density is in [0.41545, 0.416846].
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
José María Grau, Antonio M. Oller-Marcén and Jonathan Sondow, On the congruence 1^m + 2^m + ... + m^m = n (mod m), with n|m, Monatshefte für Mathematik, Vol. 177, No. 3 (2015), pp. 421-436, preprint, arXiv:1309.7941 [math.NT], 2013-2014.
MATHEMATICA
g[n_] := Mod[Sum[PowerMod[i, n, n], {i, n}], n]; Select[Range[500], !g[2*#] == # &]
CROSSREFS
Cf. A031971.
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: A133006 A055264 A113502 * A356453 A061904 A206284
KEYWORD
nonn
AUTHOR
STATUS
approved