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 A126212 #15 Apr 01 2021 12:16:06 %S A126212 1,3,1,3,1,6,1,7,4,3,1,16,1,3,4,7,1,12,1,12,4,3,1,24,6,3,4,7,1,17,1, %T A126212 15,4,3,6,25,1,3,4,20,1,12,1,7,18,3,1,24,1,18,4,7,1,21,6,15,4,3,1,43, %U A126212 1,3,13,15,6,12,1,7,4,25,1,45,1,3,9,7,8,12,1,30,13,3,1,35,6,3,4,15,1,36,8 %N A126212 a(n) = sum of the divisors of n which equal any d(k) for 1<=k<=n, where d(k) is the number of positive divisors of k. %H A126212 Antti Karttunen, <a href="/A126212/b126212.txt">Table of n, a(n) for n = 1..16384</a> %e A126212 The number of divisors of the integers 1 through 10 form the sequence 1,2,2,3,2,4,2,4,3,4. The divisors of 10 are 1,2,5,10. The divisors of 10 which occur in the sequence of d(k)'s, 1<=k<=10, are 1 and 2. So a(10) = 1+2 = 3. %t A126212 f[n_] :=Plus @@ Select[Divisors[n], MemberQ[Table[Length@Divisors[k], {k, n}], # ] &];Table[f[n], {n, 91}] (* _Ray Chandler_, Dec 21 2006 *) %o A126212 (PARI) A126212(n) = sumdiv(n,d,my(s=0); for(k=1,n,if(numdiv(k)==d,s++;break)); (d*s)); \\ _Antti Karttunen_, Apr 01 2021 %Y A126212 Cf. A000005, A126213. %Y A126212 Cf. also A126131. %K A126212 nonn %O A126212 1,2 %A A126212 _Leroy Quet_, Dec 20 2006 %E A126212 Extended by _Ray Chandler_, Dec 21 2006