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 A359270 #19 Aug 16 2023 02:27:21 %S A359270 0,0,1,0,0,1,1,0,1,0,1,1,0,0,3,0,0,1,1,0,1,0,2,2,0,0,2,0,0,1,2,0,2,0, %T A359270 1,1,1,0,3,0,0,2,1,0,1,0,2,1,0,1,4,0,0,1,2,0,1,0,1,2,0,0,4,0,1,1,1,0, %U A359270 3,0,2,1,0,0,2,1,0,2,3,0,1,0,1,1,0,0,5,1,1,1 %N A359270 Number of divisors of 5*n-3 of form 5*k+3. %C A359270 Also number of divisors of 5*n-3 of form 5*k+4. %H A359270 Seiichi Manyama, <a href="/A359270/b359270.txt">Table of n, a(n) for n = 1..10000</a> %F A359270 a(n) = A001878(5*n-3) = A001899(5*n-3). %F A359270 G.f.: Sum_{k>0} x^(3*k)/(1 - x^(5*k-1)). %F A359270 G.f.: Sum_{k>0} x^(4*k-1)/(1 - x^(5*k-2)). %t A359270 a[n_] := DivisorSum[5*n-3, 1 &, Mod[#, 5] == 3 &]; Array[a, 100] (* _Amiram Eldar_, Aug 16 2023 *) %o A359270 (PARI) a(n) = sumdiv(5*n-3, d, d%5==3); %o A359270 (PARI) a(n) = sumdiv(5*n-3, d, d%5==4); %o A359270 (PARI) my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/(1-x^(5*k-1))))) %o A359270 (PARI) my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(4*k-1)/(1-x^(5*k-2))))) %Y A359270 Cf. A001878, A001899, A359237. %K A359270 nonn,easy %O A359270 1,15 %A A359270 _Seiichi Manyama_, Dec 23 2022