A325794 - OEIS

%I #8 May 28 2019 19:38:57

%S 1,1,0,1,-1,1,-2,1,-1,0,-3,2,-4,-1,-1,1,-5,1,-6,1,-2,-2,-7,3,-3,-3,-2,

%T 0,-8,2,-9,1,-3,-4,-3,3,-10,-5,-4,2,-11,1,-12,-1,-1,-6,-13,4,-5,-1,-5,

%U -2,-14,1,-4,1,-6,-7,-15,5,-16,-8,-2,1,-5,0,-17,-3,-7

%N Number of divisors of n minus the sum of prime indices of n.

%C 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).

%H Antti Karttunen, <a href="/A325794/b325794.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000005(n) - A056239(n).

%t Table[DivisorSigma[0,n]-Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]*k]],{n,100}]

%o (PARI)

%o A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }

%o A325794(n) = (numdiv(n)-A056239(n)); \\ _Antti Karttunen_, May 26 2019

%Y Positions of positive terms are A325795.

%Y Positions of nonnegative terms are A325796.

%Y Positions of negative terms are A325797.

%Y Positions of nonpositive terms are A325798.

%Y Positions of 1's are A325792.

%Y Positions of 0's are A325793.

%Y Positions of -1's are A325694.

%Y Cf. A000005, A002033, A056239, A112798, A299702, A325780, A325781.

%K sign,look,hear

%O 1,7

%A _Gus Wiseman_, May 23 2019