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 A232099 #40 Dec 12 2013 03:18:05
%S A232099 840,2520,4200,5880,7560,9240,10920,12600,14280,15960,17640,19320,
%T A232099 21000,22680,24360,26040,27720,29400,31080,32760,34440,36120,37800,
%U A232099 39480,41160,42840,44520,46200,47880,49560,51240,52920,54600,55440,56280,57960,59640,61320,63000
%N A232099 Numbers n such that {largest m such that 1, 2, ..., m divide n} is different from {largest m such that m! divides n^2}.
%C A232099 Numbers n such that A055874(n) differs from A232098(n). (By the definition of the sequence).
%C A232099 This sequence is a subset of A055926. Please see there for a proof. From that follows that A055881(a(n))+1 is always composite (in range n=1..100000, only values 6, 8, 9 and 10 occur).
%C A232099 Also, incidentally, for the first five terms, n=1..5, a(n) = 70*A055926(n), then a(6)=77*A055926(6), and the next time the ratio A232099(n)/A055926(n) is integral is at n=21, where a(n) = 82*A055926(21), at n=41 (a(41) = 79*A055926(41) = 79*840 = 66360), at n=136, a(136) = 80*A055926(136) = 80*2772 = 221760 and at n=1489, where a(1489) = 80*A055926(1489) = 80 * 30492 = 2439360. The ratio seems to converge towards some value a little less than 80. Please see the plot generated by Plot2 in the links section.
%H A232099 Antti Karttunen, <a href="/A232099/b232099.txt">Table of n, a(n) for n = 1..10000</a>
%H A232099 OEIS Server, <a href="https://oeis.org/plot2a?name1=A232099&name2=A055926&tform1=untransformed&tform2=untransformed&shift=0&radiop1=ratio&drawlines=true">Ratio A232099(n)/A055926(n) plotted with Plot 2</a>
%H A232099 OEIS Server, <a href="https://oeis.org/plot2a?name1=A232099&name2=A232743&tform1=untransformed&tform2=untransformed&shift=0&radiop1=ratio&drawlines=true">Ratio A232099(n)/A232743(n) plotted with Plot 2</a>
%H A232099 Wikipedia, <a href="http://en.wikipedia.org/wiki/Wilsons_theorem">Wilson's theorem</a> (Please see especially the section "Composite modulus")
%F A232099 For all n, a(n) = A055926(A232100(n)). [Follows from the definition of A232100, but cannot as such be used to compute the sequence. Use the given Scheme-program instead.]
%e A232099 840 (= 3*5*7*8) is in the sequence as all natural numbers up to 8 divide 840, but the largest factorial that divides its square, 705600, is 7! (840^2 = 140 * 5040), and 7 differs from 8.
%o A232099 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A232099 (define A232099 (MATCHING-POS 1 1 (lambda (n) (not (= (A232098 n) (A055874 n))))))
%Y A232099 Subset of A055926.
%Y A232099 Cf. A055881, A055874, A232098, A232100.
%K A232099 nonn
%O A232099 1,1
%A A232099 _Antti Karttunen_, Nov 18 2013