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 A300385 #22 Oct 07 2018 19:31:30
%S A300385 0,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,2,1,2,1,1,1,4,1,1,1,2,1,3,1,4,1,1,
%T A300385 1,6,1,1,1,5,1,3,1,2,2,1,1,11,1,2,1,2,1,5,1,5,1,1,1,9,1,1,2,11,1,3,1,
%U A300385 2,1,3,1,19,1,1,2,2,1,3,1,14,2,1,1,10,1,1,1,5,1,10,1,2,1,1,1,33,1,2,2,7,1,3,1,5,3
%N A300385 In the ranked poset of integer partitions ordered by refinement, number of maximal chains from the partition with Heinz number n to the local maximum.
%C A300385 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A300385 Antti Karttunen, <a href="/A300385/b300385.txt">Table of n, a(n) for n = 1..12288</a>
%H A300385 Antti Karttunen, <a href="/A300385/a300385.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%H A300385 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A300385 <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>
%F A300385 a(1) = 0; for n > 1, if A001222(n) <= 2 [when n is a prime or semiprime], a(n) = 1, otherwise, a(n) = Sum_{p|n} Sum_{q|n, q>=(p+[p^2 does not divide n])} a(prime(primepi(p)+primepi(q)) * (n/(p*q))), where p ranges over all distinct primes dividing n, and q also ranges over primes dividing n, but with condition that q > p if p is a unitary prime factor of n, otherwise q >= p. Here primepi = A000720. - _Antti Karttunen_, Oct 07 2018
%e A300385 The a(36) = 6 maximal chains are the rows:
%e A300385 (2211)<(222)<(42)<(6)
%e A300385 (2211)<(411)<(42)<(6)
%e A300385 (2211)<(411)<(51)<(6)
%e A300385 (2211)<(321)<(42)<(6)
%e A300385 (2211)<(321)<(51)<(6)
%e A300385 (2211)<(321)<(33)<(6)
%t A300385 chc[ptn_]:=If[Length[ptn]===1,1,Total[chc/@Union[ReplaceList[ptn,{a___,x_,b___,y_,c___}:>Sort[{x+y,a,b,c},Greater]]]]];
%t A300385 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A300385 Table[chc[Reverse[primeMS[n]]],{n,100}]
%o A300385 (PARI) A300385(n) = if(1==n,0,if(bigomega(n)<=2,1,my(f=factor(n), u = #f~, s = 0); for(i=1,u,for(j=i+(1==f[i,2]),u, s += A300385((n/(f[i,1]*f[j,1])*prime(primepi(f[i,1])+primepi(f[j,1])))))); (s))); \\ _Antti Karttunen_, Oct 06 2018
%o A300385 (PARI)
%o A300385 memoA300385 = Map();
%o A300385 A300385(n) = if(1==n,0,if(bigomega(n)<=2,1,if(mapisdefined(memoA300385,n),mapget(memoA300385,n),my(f=factor(n), u = #f~, s = 0); for(i=1,u,for(j=i+(1==f[i,2]),u, s += A300385(prime(primepi(f[i,1])+primepi(f[j,1]))*(n/(f[i,1]*f[j,1]))))); mapput(memoA300385,n,s); (s)))); \\ (A memoized implementation). - _Antti Karttunen_, Oct 07 2018
%Y A300385 Cf. A000041, A001055, A001222, A002846, A056239, A112798, A213427, A215366, A265947, A296150, A299200, A299202, A299925, A300273, A300383, A300384.
%K A300385 nonn
%O A300385 1,12
%A A300385 _Gus Wiseman_, Mar 04 2018
%E A300385 More terms from _Antti Karttunen_, Oct 06 2018