cp's OEIS Frontend

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.

A325163 Heinz number of the inner lining partition of the integer partition with Heinz number n.

This page as a plain text file.
%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