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
Amiram Eldar, Table of n, a(n) for n = 1..10000
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.
KEYWORD
nonn
AUTHOR
José María Grau Ribas, Sep 24 2013
STATUS
approved