A325224 - OEIS

%I #5 Apr 13 2019 08:11:07

%S 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 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 7,5,18,6,9,5,19,5,20,11,5,7,7,6,21,4,6,12

%N 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 A prime index of n is a number m such that prime(m) divides n.

%C 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 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000533">St000533: The maximal number of non-attacking rooks on a Ferrers shape</a>

%F a(n) = A056239(n) - min(A001222(n), A061395(n)) = A056239(n) - A325225(n).

%e 88 has 4 prime indices {1,1,1,5} with sum 8 and maximum 5, so a(88) = 8 - min(4,5) = 4.

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Table[If[n==1,0,Total[primeMS[n]]-Min[Length[primeMS[n]],Max[primeMS[n]]]],{n,100}]

%Y The number of times k appears in the sequence is A325232(k).

%Y Cf. A001222, A052126, A056239, A061395, A064989, A065770, A112798, A174090, A257990, A263297, A325134, A325169, A325223, A325225, A325227.

%K nonn

%O 1,5

%A _Gus Wiseman_, Apr 12 2019