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 A386546 #8 Jul 30 2025 00:28:15
%S A386546 1,2,6,9,12,18,21,26,28,31,43,49,52,54,73,79,91,93,95,99,102,109,111,
%T A386546 121,122,133,153,159,175,179,185,193,197,211,215,227,231,239,241,243,
%U A386546 271,279,286,291,295,299,301,305,309,311,313,318,324,329,339,345
%N A386546 Numbers k >= 1 such that k = d(k) + d(k+1) + ... + d(k+r) for some r >= 0 where d(i) is the number of divisors of i (A000005).
%C A386546 r is from {0,0,1,2,2,3,4,5,5,6,8,9,9,13,13,13,16,15,15,...}.
%e A386546 For k = 2: 2 = A000005(2) = 2, thus 2 is a term.
%e A386546 For k = 6: 6 = A000005(6) + A000005(7) = 4 + 2 = 6, thus 6 is a term.
%t A386546 q[k_] := Module[{s = 0, m = k}, While[s < k, s += DivisorSigma[0, m]; m++]; s == k]; Select[Range[350], q] (* _Amiram Eldar_, Jul 25 2025 *)
%Y A386546 Cf. A000005.
%K A386546 nonn
%O A386546 1,2
%A A386546 _Ctibor O. Zizka_, Jul 25 2025