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 A325163 #5 Apr 05 2019 09:29:10 %S A325163 1,2,3,3,5,5,7,5,10,7,11,7,13,11,14,7,17,14,19,11,22,13,23,11,21,17, %T A325163 21,13,29,22,31,11,26,19,33,22,37,23,34,13,41,26,43,17,33,29,47,13,55, %U A325163 33,38,19,53,33,39,17,46,31,59,26,61,37,39,13,51,34,67,23 %N A325163 Heinz number of the inner lining partition of the integer partition with Heinz number n. %C A325163 The k-th part of the inner lining partition of an integer partition is the number of squares in its Young diagram that are k diagonal steps from the lower-right boundary. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). %e A325163 The partition with Heinz number 7865 is (6,5,5,3), with diagram %e A325163 o o o o o o %e A325163 o o o o o %e A325163 o o o o o %e A325163 o o o %e A325163 which has diagonal distances %e A325163 3 3 3 2 1 1 %e A325163 3 2 2 2 1 %e A325163 2 2 1 1 1 %e A325163 1 1 1 %e A325163 so the inner lining partition is (9,6,4), which has Heinz number 2093, so a(7865) = 2093. %t A325163 Table[Times@@Prime/@(-Differences[Total/@Take[FixedPointList[If[#=={},{},DeleteCases[Rest[#]-1,0]]&,Reverse[Flatten[Cases[If[n==1,{},FactorInteger[n]],{p_,k_}:>Table[PrimePi[p],{k}]]]]],{1,-2}]]),{n,100}] %Y A325163 Cf. A052126, A056239, A064989, A065770, A093641, A112798, A188674, A252464, A257990, A297113, A325133, A325135, A325164, A325167, A325169. %K A325163 nonn %O A325163 1,2 %A A325163 _Gus Wiseman_, Apr 05 2019