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 A328898 #28 Apr 12 2020 21:44:32
%S A328898 0,1,1,6,1,11,1,28,12,27,1,58,1,51,28,120,1,105,1,154,52,123,1,260,30,
%T A328898 171,117,298,1,281,1,496,124,291,54,534,1,363,172,708,1,545,1,730,309,
%U A328898 531,1,1096,56,685,292,1018,1,963,126,1380,364,843,1,1462,1,963,597,2016,174,1337,1,1738,532,1333,1,2364,1,1371,715,2170,128,1865
%N A328898 Sum of p-ary comparisons units required to rank a sequence in parallel when the sequence is partitioned into heaps equal to the prime factors p of the initial sequence length n.
%C A328898 a(1) = 0.
%C A328898 1 <= a(n) <= (n^2-n)/2 for all n>1.
%C A328898 a(n) = (n^2-n)/2, if n is a power of 2.
%C A328898 a(n) = 1, if n is a prime number.
%H A328898 Antti Karttunen, <a href="/A328898/b328898.txt">Table of n, a(n) for n = 1..32768</a>
%H A328898 Jonathan Blanchette and Robert Laganière, <a href="https://arxiv.org/abs/1910.11749">A Curious Link Between Prime Numbers, the Maundy Cake Problem and Parallel Sorting</a>, arXiv:1910.11749 [cs.DS], 2019.
%F A328898 a(n) = n^2*Sum_{i=1..m} 1/(f(i)^2*f(i-1)*f(i-2)*...*f(1)) where f(i) is the i-th prime factor of n with repetition and m is the number of prime factors.
%F A328898 a(n) = n^2*Sum_{p(i)}(1/p(i) * 1/(Product_{j=1..i} p(j)^k(j)) * (p(i)^k(i)-1)/(p(i)-1)) where p(i) is the i-th unique prime factor of n with multiplicity k(i) and p(i)<p(i+1).
%o A328898 (PARI) a(n) = my(f=factor(n)); n^2*sum(i=1, #f~, (1/f[i,1]) * (1/(prod(j=1, i, f[j,1]^f[j,2]))) * (f[i,1]^f[i,2]-1)/(f[i,1]-1)); \\ _Michel Marcus_, Oct 31 2019
%Y A328898 Cf. A006022.
%K A328898 nonn
%O A328898 1,4
%A A328898 _Jonathan Blanchette_, Oct 30 2019
%E A328898 More terms from _Antti Karttunen_, Apr 12 2020