cp's OEIS Frontend

A321650 Irregular triangle whose n-th row is the reversed conjugate of the integer partition with Heinz number n.

%I A321650 #5 Nov 15 2018 21:12:09
%S A321650 1,1,1,2,1,1,1,1,2,1,1,1,1,3,2,2,1,1,2,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,
%T A321650 1,2,1,2,2,4,1,1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,1,1,3,1,1,2,2,1,1,1,1,
%U A321650 2,1,1,1,1,1,1,1,1,1,1,4,2,2,2,1,1,1,1
%N A321650 Irregular triangle whose n-th row is the reversed conjugate of the integer partition with Heinz number n.
%C A321650 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%F A321650 a(n,i) = A112798(A122111(n),i).
%e A321650 Triangle begins:
%e A321650   1
%e A321650   1 1
%e A321650   2
%e A321650   1 1 1
%e A321650   1 2
%e A321650   1 1 1 1
%e A321650   3
%e A321650   2 2
%e A321650   1 1 2
%e A321650   1 1 1 1 1
%e A321650   1 3
%e A321650   1 1 1 1 1 1
%e A321650   1 1 1 2
%e A321650   1 2 2
%e A321650   4
%e A321650   1 1 1 1 1 1 1
%e A321650   2 3
%e A321650   1 1 1 1 1 1 1 1
%e A321650   1 1 3
%e A321650   1 1 2 2
%e A321650   1 1 1 1 2
%e A321650   1 1 1 1 1 1 1 1 1
%e A321650 The sequence of reversed dual partitions begins: (), (1), (11), (2), (111), (12), (1111), (3), (22), (112), (11111), (13), (111111), (1112), (122), (4), (1111111), (23), (11111111), (113), (1122), (11112), (111111111), (14), (222), (111112), (33), (1113), (1111111111), (123).
%t A321650 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A321650 conj[y_]:=If[Length[y]==0,y,Table[Length[Select[y,#>=k&]],{k,1,Max[y]}]];
%t A321650 Table[Sort[conj[primeMS[n]]],{n,50}]
%Y A321650 Cf. A008480, A056239, A112798, A122111, A296150, A321648, A321649.
%K A321650 nonn,tabf
%O A321650 1,4
%A A321650 _Gus Wiseman_, Nov 15 2018