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 A061117 #15 Feb 02 2025 14:04:13
%S A061117 3,4,4,6,5,6,6,8,8,9,8,8,6,10,8,12,8,8,12,8,10,12,12,9,8,8,12,10,16,8,
%T A061117 12,8,15,12,12,12,8,16,10,18,8,14,9,12,16,16,12,12,8,12,20,8,18,12,16,
%U A061117 16,12,16,8,18,18,12,16,12,16,20,12,12,12,8,24,12,16,12,16,18,15,16,12
%N A061117 Maximum number of divisors for any composite between prime(n) and prime(n+1).
%H A061117 Michael De Vlieger, <a href="/A061117/b061117.txt">Table of n, a(n) for n = 2..10000</a> (terms up to n = 1000 by Harry J. Smith)
%F A061117 a(n) = Max{d(c); p(n+1) > c > p(n)}, c is composite, p(n) is the n-th prime and d=A000005().
%e A061117 p(30)=113 is followed by 13 composites; numbers of divisors are {8, 4, 6, 6, 4, 4, 16, 3, 4, 4, 6, 4, 12}; the smallest is 4=a(30) and the largest is 16.
%t A061117 Max /@ DivisorSigma[0, Select[SplitBy[Range@ Prime@ 81, PrimeQ], CompositeQ@ First@ # &]] (* _Michael De Vlieger_, Nov 02 2017 *)
%t A061117 Table[Max[DivisorSigma[0,Range[p+1,NextPrime[p]-1]]],{p,Prime[Range[2,80]]}] (* _Harvey P. Dale_, Feb 02 2025 *)
%o A061117 (PARI) { n=-1; q=3; forprime (p=5, prime(1003), a=0; for (i=q + 1, p - 1, a=max(numdiv(i), a)); q=p; write("b061117.txt", n++, " ", a) ) } \\ _Harry J. Smith_, Jul 18 2009
%Y A061117 Cf. A000005, A061112.
%K A061117 nonn
%O A061117 2,1
%A A061117 _Labos Elemer_, May 29 2001