A343938 Twice the number of prime factors of n minus the sum of prime indices of n, both counted with multiplicity.

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

Offset: 1

Author

Gus Wiseman, Aug 04 2021

Keywords

• sign

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.

Examples

			For n = 1050 we have 5 prime indices {1,2,3,3,4}, so a(1050) = 10 - 13 = -3.
		

Crossrefs

First appearances are the elements of A174090 except for 3.

Positions of zeros are A340387.

Positions of nonpositive terms are A344291.

Positions of nonnegative terms are A344296.

A001222 counts prime indices.

A056239 adds up prime indices.

A112798 lists prime indices.

Cf. A001221, A003963, A061775, A275024, A279789, A299757, A302242.

Programs

Mathematica

Table[2*PrimeOmega[n]-Total[Cases[FactorInteger[n],{p_,k_}:>k*PrimePi[p]]],{n,100}]

Formula

Totally additive with a(prime(k)) = 2 - k.