OFFSET
1,20
LINKS
FORMULA
G.f.: Sum_{k>=1} x^(10*k) / (1 - x^k).
L.g.f.: -log( Product_{k>=10} (1 - x^k)^(1/k) ).
G.f.: Sum_{k>=10} x^k/(1 - x^k). - Seiichi Manyama, Jan 07 2023
Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 9649/2520), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 08 2024
MATHEMATICA
Table[DivisorSum[n, 1 &, # > 9 &], {n, 1, 110}]
nmax = 110; CoefficientList[Series[Sum[x^(10 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 1] &
nmax = 110; CoefficientList[Series[-Log[Product[(1 - x^k)^(1/k), {k, 10, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Drop[#, 1] &
PROG
(PARI) a(n) = sumdiv(n, d, d>9); \\ Michel Marcus, Apr 22 2021
(PARI) my(N=100, x='x+O('x^N)); concat([0, 0, 0, 0, 0, 0, 0, 0, 0], Vec(sum(k=10, N, x^k/(1-x^k)))) \\ Seiichi Manyama, Jan 07 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Apr 22 2021
EXTENSIONS
a(1)-a(9) prepended by David A. Corneth, Jun 13 2022
STATUS
approved