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.
%I A357458 #9 Jul 23 2025 16:04:13
%S A357458 0,1,-1,2,-1,1,-2,2,0,1,-2,2,-1,1,-3,4,-2,1,-1,1,0,1,-3,3,-1,0,-1,2,
%T A357458 -1,2,-5,4,0,0,-2,2,-1,1,-2,4,-3,2,-2,1,0,1,-4,3,0,1,-2,1,-1,2,-3,2,0,
%U A357458 3,-4,2,0,-1,-4,5,-1,4,-4,1,-1,1,-3,4,-2,1,-2,2
%N A357458 First differences of A325033 = "Sum of sums of the multiset of prime indices of each prime index of n.".
%C A357458 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. The multiset of multisets with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset of multisets with MM-number 78 is {{},{1},{1,2}}.
%F A357458 a(n) = A325033(n + 1) - A325033(n).
%e A357458 We have A325033(5) - A325033(4) = 2 - 0, so a(4) = 2.
%t A357458 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A357458 Differences[Table[Plus@@Join@@primeMS/@primeMS[n],{n,100}]]
%Y A357458 The partial sums are A325033, which has row-products A325032.
%Y A357458 The version for standard compositions is A357187.
%Y A357458 A000961 lists prime powers.
%Y A357458 A003963 multiples prime indices.
%Y A357458 A005117 lists squarefree numbers.
%Y A357458 A056239 adds up prime indices.
%Y A357458 Cf. A000720, A001221, A001222, A007716, A109082, A275024, A302242, A302243, A302505, A324926, A325034, A357139.
%K A357458 sign
%O A357458 1,4
%A A357458 _Gus Wiseman_, Sep 30 2022