cp's OEIS Frontend

A325799 Sum of the prime indices of n minus the number of distinct positive subset-sums of the prime indices of n.

%I A325799 #10 May 28 2019 19:39:03
%S A325799 0,0,1,0,2,0,3,0,2,1,4,0,5,2,2,0,6,0,7,0,3,3,8,0,4,4,3,1,9,0,10,0,4,5,
%T A325799 4,0,11,6,5,0,12,0,13,2,2,7,14,0,6,2,6,3,15,0,5,0,7,8,16,0,17,9,4,0,6,
%U A325799 1,18,4,8,2,19,0,20,10,3,5,6,2,21,0,4,11
%N A325799 Sum of the prime indices of n minus the number of distinct positive subset-sums of the prime indices of n.
%C A325799 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, with sum A056239(n). A positive subset-sum of an integer partition is any sum of a nonempty submultiset of it.
%F A325799 a(n) = A056239(n) - A304793(n).
%e A325799 The prime indices of 21 are {2,4}, with positive subset-sums {2,4,6}, so a(21) = 6 - 3 = 3.
%t A325799 hwt[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p] k]];
%t A325799 Table[hwt[n]-Length[Union[hwt/@Rest[Divisors[n]]]],{n,30}]
%Y A325799 Positions of 1's are A325800.
%Y A325799 Positions of nonzero terms are A325798.
%Y A325799 Cf. A000005, A002033, A056239, A108917, A112798, A276024, A299702, A304793.
%Y A325799 Cf. A325694, A325780, A325794, A325801, A325802.
%K A325799 nonn
%O A325799 1,5
%A A325799 _Gus Wiseman_, May 23 2019