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 A294651 #74 Jan 15 2021 21:31:52 %S A294651 1,6,15,20,24,28,33,40,48,52,65,65,75,76,85,88,91,100,105,115,115,119, %T A294651 132,140,144,145,155,161,162,171,217,174,182,190,195,196,296,200,207, %U A294651 220,246,224,301,231,238,253,329,275,280,287,288,296,371,300,304,305 %N A294651 Least possible value for the highest denominator in the decomposition of unity as a sum of different unitary fractions the greatest of which is 1/n. %C A294651 The decompositions need not be unique. E.g., for a(7) either 1/12 or 1/20 + 1/30 may be used in the decomposition indifferently. %C A294651 For prime numbers p and any fixed epsilon < 1, a(p) > epsilon*p*log(p) for all sufficiently large p. %H A294651 Jon E. Schoenfield, <a href="/A294651/a294651_4.txt">All unitary decompositions (listed in lexicographic order) for n = 1..30</a>. (Decompositions up to n = 18 originally found by J. Múgica.) %H A294651 Javier Múgica, Values of <a href="/A294651/a294651_5.txt">a(n)/n</a>. %e A294651 1 = 1/3 + 1/4 + 1/6 + 1/10 + 1/12 + 1/15, and there is no such decomposition starting at 1/3 and having a greatest denominator smaller than 15, so a(3)=15. %Y A294651 Cf. A192881, which looks at decompositions with the least possible number of terms. Those from this sequence achieve those bounds up to a(7), with exception of a(3). However, n=7 is likely the last value of n for which this holds. %Y A294651 Cf. A272083. %K A294651 nonn,nice %O A294651 1,2 %A A294651 _Javier Múgica_, Nov 06 2017 %E A294651 a(18)-a(24) from _Jon E. Schoenfield_, Dec 22 2019 %E A294651 a(25)-a(56) from _Jon E. Schoenfield_, Jan 01 2020