cp's OEIS Frontend

A358136 Irregular triangle read by rows whose n-th row lists the partial sums of the prime indices of n (row n of A112798).

%I A358136 #6 Oct 31 2022 22:05:44
%S A358136 1,2,1,2,3,1,3,4,1,2,3,2,4,1,4,5,1,2,4,6,1,5,2,5,1,2,3,4,7,1,3,5,8,1,
%T A358136 2,5,2,6,1,6,9,1,2,3,5,3,6,1,7,2,4,6,1,2,6,10,1,3,6,11,1,2,3,4,5,2,7,
%U A358136 1,8,3,7,1,2,4,6,12,1,9,2,8,1,2,3,6,13
%N A358136 Irregular triangle read by rows whose n-th row lists the partial sums of the prime indices of n (row n of A112798).
%C A358136 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 A358136 Triangle begins:
%e A358136    2: 1
%e A358136    3: 2
%e A358136    4: 1 2
%e A358136    5: 3
%e A358136    6: 1 3
%e A358136    7: 4
%e A358136    8: 1 2 3
%e A358136    9: 2 4
%e A358136   10: 1 4
%e A358136   11: 5
%e A358136   12: 1 2 4
%e A358136   13: 6
%e A358136   14: 1 5
%e A358136   15: 2 5
%e A358136   16: 1 2 3 4
%e A358136   17: 7
%e A358136   18: 1 3 5
%t A358136 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A358136 Table[Accumulate[primeMS[n]],{n,30}]
%Y A358136 Row-lengths are A001222.
%Y A358136 First element in each row is A055396.
%Y A358136 Last element in each row is A056239.
%Y A358136 Rows are the partial sums of rows of A112798.
%Y A358136 Row-sums are A318283.
%Y A358136 Sorted Heinz numbers of the rows are A325362.
%Y A358136 The version for standard compositions is A358134.
%Y A358136 Rows are ranked by A358137.
%Y A358136 A000041 counts partitions, strict A000009.
%Y A358136 A003963 multiplies prime indices.
%Y A358136 A056239 adds up prime indices.
%Y A358136 Cf. A000720, A001221, A355536, A358133.
%K A358136 nonn,tabf
%O A358136 2,2
%A A358136 _Gus Wiseman_, Oct 31 2022