cp's OEIS Frontend

A357139 Take the weakly increasing prime indices of each prime index of n, then concatenate.

%I A357139 #9 Sep 29 2022 22:05:36
%S A357139 1,2,1,1,1,1,1,2,3,1,1,2,1,1,1,2,4,1,1,1,1,1,2,1,1,1,3,2,2,1,2,2,1,2,
%T A357139 1,1,1,1,1,1,3,1,2,5,1,3,4,2,1,1,1,1,1,1,2,1,1,1,1,1,2,2,6,1,1,1,1,4,
%U A357139 3,1,1,2,2,2,2,3,1,1,1,1,1,2,2,1,4,1,2
%N A357139 Take the weakly increasing prime indices of each prime index of n, then concatenate.
%C A357139 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 A357139 Triangle begins:
%e A357139    1:
%e A357139    2:
%e A357139    3:  1
%e A357139    4:
%e A357139    5:  2
%e A357139    6:  1
%e A357139    7:  1 1
%e A357139    8:
%e A357139    9:  1 1
%e A357139   10:  2
%e A357139   11:  3
%e A357139   12:  1
%e A357139   13:  1 2
%e A357139 For example, the weakly increasing prime indices of 105 are (2,3,4), with prime indices ((1),(2),(1,1)), so row 105 is (1,2,1,1).
%t A357139 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A357139 Join@@Table[Join@@primeMS/@primeMS[n],{n,100}]
%Y A357139 Row lengths are A302242.
%Y A357139 Positions of strict rows are A302505.
%Y A357139 Positions of constant rows are A302593.
%Y A357139 Row sums are A325033, products A325032.
%Y A357139 The version for standard compositions is A357135, rank A357134.
%Y A357139 A000961 lists prime powers.
%Y A357139 A003963 multiples prime indices.
%Y A357139 A056239 adds up prime indices.
%Y A357139 Cf. A000720, A001221, A001222, A007716, A058891, A109082, A275024, A302243, A324926, A325034.
%K A357139 nonn,tabf
%O A357139 1,2
%A A357139 _Gus Wiseman_, Sep 29 2022