This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338653 #31 Jan 09 2025 10:53:11
%S A338653 0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,3,1,2,2,2,
%T A338653 1,3,1,2,2,3,1,3,1,3,2,2,1,4,1,3,2,3,1,3,2,3,2,2,1,6,1,2,2,3,2,4,1,3,
%U A338653 2,4,1,5,1,2,3,3,2,4,1,5,2,2,1,6,2,2,2,4,1,6,2,3,2,2,2,6,1,3,3,5,1,4,1,4,4,2,1,6,1,5
%N A338653 Number of divisors of n which are greater than 9.
%H A338653 Seiichi Manyama, <a href="/A338653/b338653.txt">Table of n, a(n) for n = 1..10000</a>
%H A338653 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>.
%F A338653 G.f.: Sum_{k>=1} x^(10*k) / (1 - x^k).
%F A338653 L.g.f.: -log( Product_{k>=10} (1 - x^k)^(1/k) ).
%F A338653 G.f.: Sum_{k>=10} x^k/(1 - x^k). - _Seiichi Manyama_, Jan 07 2023
%F A338653 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
%t A338653 Table[DivisorSum[n, 1 &, # > 9 &], {n, 1, 110}]
%t A338653 nmax = 110; CoefficientList[Series[Sum[x^(10 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 1] &
%t A338653 nmax = 110; CoefficientList[Series[-Log[Product[(1 - x^k)^(1/k), {k, 10, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Drop[#, 1] &
%t A338653 Table[Count[Divisors[n],_?(#>9&)],{n,120}] (* _Harvey P. Dale_, Jan 09 2025 *)
%o A338653 (PARI) a(n) = sumdiv(n, d, d>9); \\ _Michel Marcus_, Apr 22 2021
%o A338653 (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
%Y A338653 Column k=10 of A135539.
%Y A338653 Cf. A000005, A001620, A023645, A032741, A321014, A338648, A338649, A338650, A338651, A338652.
%K A338653 nonn,easy
%O A338653 1,20
%A A338653 _Ilya Gutkovskiy_, Apr 22 2021
%E A338653 a(1)-a(9) prepended by _David A. Corneth_, Jun 13 2022