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Remainder of tau(n) modulo 6.
1

%I #14 Jul 11 2024 01:23:51

%S 1,2,2,3,2,4,2,4,3,4,2,0,2,4,4,5,2,0,2,0,4,4,2,2,3,4,4,0,2,2,2,0,4,4,

%T 4,3,2,4,4,2,2,2,2,0,0,4,2,4,3,0,4,0,2,2,4,2,4,4,2,0,2,4,0,1,4,2,2,0,

%U 4,2,2,0,2,4,0,0,4,2,2,4,5,4,2,0,4,4,4,2,2,0,4,0,4,4,4,0,2,0,0,3,2,2,2,2,2

%N Remainder of tau(n) modulo 6.

%C The sums of the first 10^k terms, for k = 1, 2, ..., are 27, 236, 2275, 22166, 220070, 2195376, 21933228, 219259514, 2192385128, 21923168052, ... . Conjecture: the asymptotic mean of this sequence is 3*zeta(3)/zeta(2) = 3 * A253905 = 2.192288... . The conjecture is true if A211337 and A211338 have an equal asymptotic density (see also A059269). - _Amiram Eldar_, Jul 11 2024

%H Antti Karttunen, <a href="/A084302/b084302.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

%F a(n) = A000005(n) modulo 6.

%t Mod[DivisorSigma[0,Range[110]],6] (* _Harvey P. Dale_, Sep 04 2020 *)

%o (PARI) A084302(n) = (numdiv(n)%6); \\ _Antti Karttunen_, Jul 07 2017

%Y Cf. A000005, A054763, A084299, A084300, A084301.

%Y Cf. A059269, A211337, A211338

%K easy,nonn

%O 1,2

%A _Labos Elemer_, Jun 02 2003