cp's OEIS Frontend

A325224 Sum of prime indices of n minus the lesser of the number of prime factors of n counted with multiplicity and the maximum prime index of n.

%I A325224 #5 Apr 13 2019 08:11:07
%S A325224 0,0,1,1,2,1,3,2,2,2,4,2,5,3,3,3,6,3,7,2,4,4,8,3,4,5,4,3,9,3,10,4,5,6,
%T A325224 5,4,11,7,6,3,12,4,13,4,4,8,14,4,6,4,7,5,15,5,6,3,8,9,16,4,17,10,5,5,
%U A325224 7,5,18,6,9,5,19,5,20,11,5,7,7,6,21,4,6,12
%N A325224 Sum of prime indices of n minus the lesser of the number of prime factors of n counted with multiplicity and the maximum prime index of n.
%C A325224 A prime index of n is a number m such that prime(m) divides n.
%C A325224 Also the number of squares in the Young diagram of the integer partition with Heinz number n after the first row or the first column, whichever is smaller, is removed. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A325224 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000533">St000533: The maximal number of non-attacking rooks on a Ferrers shape</a>
%F A325224 a(n) = A056239(n) - min(A001222(n), A061395(n)) = A056239(n) - A325225(n).
%e A325224 88 has 4 prime indices {1,1,1,5} with sum 8 and maximum 5, so a(88) = 8 - min(4,5) = 4.
%t A325224 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325224 Table[If[n==1,0,Total[primeMS[n]]-Min[Length[primeMS[n]],Max[primeMS[n]]]],{n,100}]
%Y A325224 The number of times k appears in the sequence is A325232(k).
%Y A325224 Cf. A001222, A052126, A056239, A061395, A064989, A065770, A112798, A174090, A257990, A263297, A325134, A325169, A325223, A325225, A325227.
%K A325224 nonn
%O A325224 1,5
%A A325224 _Gus Wiseman_, Apr 12 2019