A084302 Remainder of tau(n) modulo 6.

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, 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, 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

Offset

1,2

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n.

Formula

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

Mathematica

Mod[DivisorSigma[0, Range[110]], 6] (* Harvey P. Dale, Sep 04 2020 *)

Prog

(PARI) A084302(n) = (numdiv(n)%6); \\ Antti Karttunen, Jul 07 2017

Crossrefs

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

Cf. A059269, A211337, A211338

Sequence in context: A332268 A355593 A355302 * A289872 A301855 A080256

Adjacent sequences: A084299 A084300 A084301 * A084303 A084304 A084305

Keyword

easy,nonn

Author

Labos Elemer, Jun 02 2003

Status

approved