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

1,7

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

Formula

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

Mathematica

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

Prog

(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

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.

Sequence in context: A161225 A174980 A277488 * A119513 A308454 A085815

Adjacent sequences: A325791 A325792 A325793 * A325795 A325796 A325797

Keyword

sign,look,hear

Author

Gus Wiseman, May 23 2019

Status

approved