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 A380958 #8 Feb 16 2025 13:36:20
%S A380958 0,0,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,1,0,0,0,2,0,0,1,1,
%T A380958 1,2,0,1,1,0,0,2,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,1,0,1,0,1,0,0,1,2,0,0,
%U A380958 1,2,0,0,0,1,0,0,1,2,0,0,0,1,0,1,1,1,1
%N A380958 Number of prime factors of n (with multiplicity) minus sum of distinct prime exponents of n.
%F A380958 a(n) = A001222(n) - A136565(n).
%e A380958 The prime factors of 2100 are {2,2,3,5,5,7}, with distinct multiplicities {1,2}, so a(2100) = 6 - (1+2) = 3.
%t A380958 Table[PrimeOmega[n]-Total[Union[Last/@If[n==1,{},FactorInteger[n]]]],{n,100}]
%Y A380958 Positions of 0's are A130091, complement A130092.
%Y A380958 The RHS (sum of distinct prime exponents) is A136565.
%Y A380958 For prime factors instead of exponents see A280292, firsts A280286, sorted A381075.
%Y A380958 For prime indices instead of exponents see A380955, firsts A380956, sorted A380957.
%Y A380958 Position of first appearance of n is A380989(n).
%Y A380958 A000040 lists the primes, differences A001223.
%Y A380958 A005117 lists squarefree numbers, complement A013929.
%Y A380958 A005361 gives product of prime signature.
%Y A380958 A055396 gives least prime index, greatest A061395.
%Y A380958 A056239 (reverse A296150) adds up prime indices, row sums of A112798, counted by A001222.
%Y A380958 A124010 lists prime exponents (signature); see A001222, A001221, A051903, A051904.
%Y A380958 Cf. A000720, A046660, A071625, A075254, A075255, A076694, A081770, A116861, A178503, A290106, A380986.
%K A380958 nonn
%O A380958 1,30
%A A380958 _Gus Wiseman_, Feb 13 2025