A293899 Number of proper divisors of the form 3k+1 minus number of proper divisors of the form 3k+2.

0, 1, 1, 0, 1, 0, 1, 1, 1, -1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, -1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, -1, 1, 1, 1, 1, 2, -1, 1, 0, 1, 1, 0, -1, 1, 1, 2, 1, 0, 1, 1, 0, -1, 1, 2, -1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 0, -1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, -1, 1, 2, -1, 1, 0, -1, 1, 0, 3, 1, 2, -1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0

Offset

1,21

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

When n = 3k, a(n) = A002324(n), when n = 3k+1, a(n) = A002324(n) - 1, when n = 3k+2, a(n) = A002324(n) + 1.

a(n) = A002324(n) - A010872(n) (mod 3).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi/(3*sqrt(3)) = 0.604599... (A073010). - Amiram Eldar, Nov 25 2023

Mathematica

Table[DivisorSum[n, 1 &, And[Mod[#, 3] == 1, # != n] &] - DivisorSum[n, 1 &, And[Mod[#, 3] == 2, # != n] &], {n, 105}] (* Michael De Vlieger, Nov 08 2017 *)
Table[Total[Which[Mod[#, 3]==1, 1, Mod[#, 3]==2, -1, True, 0]&/@Most[ Divisors[ n]]], {n, 110}] (* Harvey P. Dale, Nov 26 2021 *)

Prog

(PARI)
A293895(n) = sumdiv(n, d, (d<n)*(1==(d%3)));
A293896(n) = sumdiv(n, d, (d<n)*(2==(d%3)));
A293899(n) = (A293895(n) - A293896(n));

Crossrefs

Cf. A002324, A010872, A073010, A293895, A293896.

Sequence in context: A204244 A083093 A334621 * A015794 A011650 A016357

Adjacent sequences: A293896 A293897 A293898 * A293900 A293901 A293902

Keyword

sign,easy

Author

Antti Karttunen, Nov 06 2017

Status

approved