cp's OEIS Frontend

A380955 Sum of prime indices of n (with multiplicity) minus sum of distinct prime indices of n.

%I A380955 #12 Feb 13 2025 18:29:43
%S A380955 0,0,0,1,0,0,0,2,2,0,0,1,0,0,0,3,0,2,0,1,0,0,0,2,3,0,4,1,0,0,0,4,0,0,
%T A380955 0,3,0,0,0,2,0,0,0,1,2,0,0,3,4,3,0,1,0,4,0,2,0,0,0,1,0,0,2,5,0,0,0,1,
%U A380955 0,0,0,4,0,0,3,1,0,0,0,3,6,0,0,1,0,0,0
%N A380955 Sum of prime indices of n (with multiplicity) minus sum of distinct prime indices of n.
%C A380955 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.
%F A380955 a(n) = A056239(n) - A066328(n).
%F A380955 Additive: a(m*n) = a(m) + a(n) if gcd(m,n) = 1.
%e A380955 The prime indices of 96 are {1,1,1,1,1,2}, with sum 7, and with distinct prime indices {1,2}, with sum 3, so a(96) = 7 - 3 = 4.
%t A380955 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A380955 Table[Total[prix[n]]-Total[Union[prix[n]]],{n,100}]
%Y A380955 Positions of 0's are A005117, complement A013929.
%Y A380955 For length instead of sum we have A046660.
%Y A380955 Positions of 1's are A081770.
%Y A380955 For factors instead of indices we have A280292, firsts A280286 (sorted A381075).
%Y A380955 A multiplicative version is A290106.
%Y A380955 Counting partitions by this statistic gives A364916.
%Y A380955 Dominates A374248.
%Y A380955 Positions of first appearances are A380956, sorted A380957.
%Y A380955 For prime multiplicities instead of prime indices we have A380958.
%Y A380955 For product instead of sum we have A380986.
%Y A380955 A000040 lists the primes, differences A001223.
%Y A380955 A055396 gives least prime index, greatest A061395.
%Y A380955 A056239 adds up prime indices, row sums of A112798, length A001222.
%Y A380955 A304038 lists distinct prime indices, sum A066328, length A001221.
%Y A380955 Cf. A000720, A071625, A075254, A075255, A116861, A124010, A136565, A178503, A325033, A325034, A366528, A366749, A379681.
%K A380955 nonn
%O A380955 1,8
%A A380955 _Gus Wiseman_, Feb 11 2025