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 A061770 #10 Apr 17 2015 09:59:27
%S A061770 0,1,2,5,7,8,9,10,11,14,17,19,21,28,35,44,58,88,95,103,110,178,179,
%T A061770 185,208,222,287,313,334,358,371,419,479,502,558,629,670,718,838,1006,
%U A061770 1118,1259,1438
%N A061770 Numbers m = a(n) > a(n-1) such that there exists a smallest integer k > 1 such that k!/(k+1)^m is an integer.
%C A061770 Original name: The least exponent m = a(n) > a(n-1) for which k is the first number where k!/(k+1)^m is an integer.
%e A061770 a(5) = 8 because the first integer k > 1 such that (k+1)^8 divides k! is k = 39, which is larger than the first integer k > 1 such that (k+1)^7 divides k! (k = 35).
%e A061770 6 is not in the sequence because the first integer k > 1 such that (k+1)^6 divides k! is k = 23, which is equal to the first integer k > 1 such that (k+1)^5 divides k!.
%t A061770 l = 0; Do[k = Max[l - 1, 1]; While[ !IntegerQ[ k! / (k + 1)^n], k++ ]; If[ k > l, l = k; Print[n] ], {n, 0, 1500} ]
%o A061770 (PARI) b(n)=k=2;while(k!%(k+1)^n,k++);k
%o A061770 print1(0,", ");for(n=1,100,if(b(n)>b(n-1),print1(n,", "))) \\ _Derek Orr_, Apr 16 2015
%Y A061770 Locations of records in A061768.
%K A061770 nonn
%O A061770 0,3
%A A061770 _Robert G. Wilson v_, Jun 21 2001
%E A061770 Name and example edited by _Derek Orr_, Apr 16 2015