A325794 Number of divisors of n minus the sum of prime indices of n.

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, 0, -8, 2, -9, 1, -3, -4, -3, 3, -10, -5, -4, 2, -11, 1, -12, -1, -1, -6, -13, 4, -5, -1, -5, -2, -14, 1, -4, 1, -6, -7, -15, 5, -16, -8, -2, 1, -5, 0, -17, -3, -7

Offset: 1

Author

Gus Wiseman, May 23 2019

Keywords

• sign
• look
• hear

Comments

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).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Positions of positive terms are A325795.

Positions of nonnegative terms are A325796.

Positions of negative terms are A325797.

Positions of nonpositive terms are A325798.

Positions of 1's are A325792.

Positions of 0's are A325793.

Positions of -1's are A325694.

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

Programs

Mathematica

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

PARI

A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
A325794(n) = (numdiv(n)-A056239(n)); \\ Antti Karttunen, May 26 2019

Formula

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