A359211 - OEIS

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A359211

a(n) = tau(3*n-1)/2, where tau(n) = number of divisors of n, cf. A000005.

1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 2, 2, 1, 3, 1, 3, 1, 4, 1, 2, 2, 3, 1, 2, 2, 5, 1, 2, 1, 3, 2, 3, 1, 4, 1, 4, 1, 3, 2, 2, 2, 4, 1, 2, 1, 6, 2, 2, 1, 4, 2, 2, 2, 3, 1, 4, 1, 5, 1, 4, 2, 3, 1, 2, 1, 6, 2, 2, 2, 3, 2, 2, 2, 6, 1, 4, 1, 3, 1, 3, 3, 4, 1, 2, 1, 6, 1, 4, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Also number of divisors of 3*n-1 of form 3*k+1 (or 3*k+2).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

FORMULA

G.f.: Sum_{k>0} x^k/(1 - x^(3*k-1)).

G.f.: Sum_{k>0} x^(2*k-1)/(1 - x^(3*k-2)).

Sum_{k=1..n} a(k) = (log(n) + 2*gamma - 1 + 2*log(3))*n/3 + O(n^(1/3)*log(n)), where gamma is Euler's constant (A001620). - Amiram Eldar, Dec 26 2022

MATHEMATICA