login
A359305
Number of divisors of 6*n-1 of form 6*k+1.
9
1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 3, 1, 2, 1, 1, 4, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 3
OFFSET
1,6
COMMENTS
Also number of divisors of 6*n-1 of form 6*k+5.
LINKS
FORMULA
a(n) = A279060(6*n-1) = A319995(6*n-1).
G.f.: Sum_{k>0} x^k/(1 - x^(6*k-1)).
G.f.: Sum_{k>0} x^(5*k-4)/(1 - x^(6*k-5)).
From Amiram Eldar, Dec 26 2022: (Start)
a(n) = A000005(A016969(n-1))/2.
Sum_{k=1..n} a(k) = (log(n) + 2*gamma - 1 + 3*log(2) + 2*log(3))*n/6 + O(n^(1/3)*log(n)), where gamma is Euler's constant (A001620). (End)
MATHEMATICA
a[n_] := DivisorSigma[0, 6*n - 1]/2; Array[a, 100] (* Amiram Eldar, Dec 26 2022 *)
PROG
(PARI) a(n) = sumdiv(6*n-1, d, d%6==1);
(PARI) a(n) = sumdiv(6*n-1, d, d%6==5);
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(6*k-1))))
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(5*k-4)/(1-x^(6*k-5))))
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 25 2022
STATUS
approved