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A356958 Triangle read by rows: if n has weakly increasing prime indices (a,b,...,y,z) then row n is (b-a+1, ..., y-a+1, z-a+1).

%I A356958 #9 Dec 28 2022 09:04:54
%S A356958 1,2,1,1,1,3,1,2,4,2,1,1,1,2,2,1,3,3,5,1,1,2,1,6,1,1,1,4,2,3,1,1,1,1,
%T A356958 4,7,2,1,2,2,8,5,1,1,3,2,4,1,5,1,2,9,1,1,1,2,1,3,3,6,1,6,2,2,2,3,1,1,
%U A356958 4,7,10,1,2,3,11,1,3,1,1,1,1,1,4,2,5
%N A356958 Triangle read by rows: if n has weakly increasing prime indices (a,b,...,y,z) then row n is (b-a+1, ..., y-a+1, z-a+1).
%C A356958 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A356958 Triangle begins:
%e A356958    1:   .
%e A356958    2:   .
%e A356958    3:   .
%e A356958    4:   1
%e A356958    5:   .
%e A356958    6:   2
%e A356958    7:   .
%e A356958    8:  1 1
%e A356958    9:   1
%e A356958   10:   3
%e A356958   11:   .
%e A356958   12:  1 2
%e A356958   13:   .
%e A356958   14:   4
%e A356958   15:   2
%e A356958   16: 1 1 1
%e A356958 For example, the prime indices of 315 are (2,2,3,4), so row 315 is (2,3,4) - 2 + 1 = (1,2,3).
%t A356958 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A356958 Table[If[n==1,{},1-First[primeMS[n]]+Rest[primeMS[n]]],{n,100}]
%Y A356958 Row lengths are A001222(n) - 1.
%Y A356958 Indices of empty rows are A008578.
%Y A356958 Even bisection is A112798.
%Y A356958 Heinz numbers of rows are A246277.
%Y A356958 An opposite version is A358172, Heinz numbers A358195.
%Y A356958 Row sums are A359358(n) + A001222(n) - 1.
%Y A356958 A112798 list prime indices, sum A056239.
%Y A356958 A243055 subtracts the least prime index from the greatest.
%Y A356958 Cf. A055396, A124010, A241916, A253565, A325351, A325352, A326844, A355534, A355536, A358137.
%K A356958 nonn,tabf
%O A356958 1,2
%A A356958 _Gus Wiseman_, Dec 27 2022