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

1,4

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.

Links

Table of n, a(n) for n=1..69.

Formula

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

Example

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

Mathematica

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

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.

Sequence in context: A191620 A214751 A306512 * A239397 A307884 A329221

Adjacent sequences: A343935 A343936 A343937 * A343939 A343940 A343941

Keyword

sign

Author

Gus Wiseman, Aug 04 2021

Status

approved