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 A328166 #10 Dec 10 2021 11:37:33
%S A328166 2,3,4,6,4,10,4,12,8,12,4,28,4,12,16,24,4,40,4,36,16,12,4,112,8,12,16,
%T A328166 48,4,120,4,48,16,12,16,224,4,12,16,144,4,120,4,48,64,12,4,448,8,48,
%U A328166 16,48,4,160,16,144,16,12,4,832,4,12,64,96,16,160,4,48,16
%N A328166 Heinz number of the run-lengths of the divisors of n.
%C A328166 The Heinz number of an integer partition or multiset {y_1,...,y_k} is prime(y_1)*...*prime(y_k).
%H A328166 Antti Karttunen, <a href="/A328166/b328166.txt">Table of n, a(n) for n = 1..20000</a>
%H A328166 Wikipedia, <a href="https://en.wikipedia.org/wiki/Run_(cards)">Run (cards)</a>
%H A328166 <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>
%F A328166 A001222(a(n)) = A137921(n).
%F A328166 A056239(a(n)) = A000005(n).
%e A328166 Splitting the divisors of 30 into runs gives {{1, 2, 3}, {5, 6}, {10}, {15}, {30}}, and the Heinz number of {1, 1, 1, 2, 3} is 120, so a(30) = 120.
%e A328166 More examples from _Antti Karttunen_, Dec 09 2021: (Start)
%e A328166 Splitting the divisors of 1 into runs gives {1}, and the Heinz number of that is 2.
%e A328166 Splitting the divisors of 2 into runs gives {1, 2}, and the Heinz number of that is 3. [one run of length 2, therefore a(2) = prime(2)^1].
%e A328166 Splitting the divisors of 3 into runs gives {1} and {3}, and the Heinz number of that is 4. [two runs of length 1, therefore a(3) = prime(1)^2].
%e A328166 Splitting the divisors of 4 into runs gives {1, 2} and {4}, and the Heinz number of that is 6. [one run of length 1, and other run of length 2, therefore a(4) = prime(1)*prime(2)].
%e A328166 Splitting the divisors of 5 into runs gives {1} and {5}, and the Heinz number of that is 4. [two runs of length 1, therefore a(5) = prime(1)^2].
%e A328166 (End)
%t A328166 Table[Times@@Prime/@Length/@Split[Divisors[n],#2==#1+1&],{n,30}]
%o A328166 (PARI) A328166(n) = { my(rl=0,pd=0,v=vector(numdiv(n)),m=1); fordiv(n, d, if(d>(1+pd), v[rl]++; rl=0); pd=d; rl++); v[rl]++; for(i=1,#v, m *= prime(i)^v[i]); (m); }; \\ _Antti Karttunen_, Dec 09 2021
%Y A328166 The longest run of divisors of n has length A055874(n).
%Y A328166 Numbers whose divisors > 1 have no non-singleton runs are A088725.
%Y A328166 The number of successive pairs of divisors of n is A129308(n).
%Y A328166 The Heinz number of the set of divisors of n is A275700(n).
%Y A328166 Numbers whose divisors do not have weakly decreasing run-lengths are A328165.
%Y A328166 Cf. A000005, A056239, A060680, A060775, A119313, A137921, A181063, A199970.
%K A328166 nonn
%O A328166 1,1
%A A328166 _Gus Wiseman_, Oct 07 2019