A330944 Number of nonprime prime indices of n.

0, 1, 0, 2, 0, 1, 1, 3, 0, 1, 0, 2, 1, 2, 0, 4, 0, 1, 1, 2, 1, 1, 1, 3, 0, 2, 0, 3, 1, 1, 0, 5, 0, 1, 1, 2, 1, 2, 1, 3, 0, 2, 1, 2, 0, 2, 1, 4, 2, 1, 0, 3, 1, 1, 0, 4, 1, 2, 0, 2, 1, 1, 1, 6, 1, 1, 0, 2, 1, 2, 1, 3, 1, 2, 0, 3, 1, 2, 1, 4, 0, 1, 0, 3, 0, 2, 1

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..87.

Formula

a(n) + A257994(n) = A001222(n).

Additive with a(p^e) = e if primepi(p) is nonprime, and 0 otherwise. - Amiram Eldar, Nov 03 2023

Example

24 has prime indices {1,1,1,2}, of which {1,1,1} are nonprime, so a(24) = 3.

Mathematica

Table[Total[Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}/; !PrimeQ[PrimePi[p]]:>k]], {n, 30}]

Prog

(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if(!isprime(primepi(f[k, 1])), f[k, 2], 0)); \\ Daniel Suteu, Jan 14 2020

Crossrefs

The number of prime prime indices is given by A257994.

Primes of prime index are A006450.

Primes of nonprime index are A007821.

Products of primes of prime index are A076610.

Products of primes of nonprime index are A320628.

Numbers whose prime indices are not all prime are A330945.

Cf. A000040, A000720, A001222, A007097, A018252, A056239, A112798, A302242, A320629, A320633, A330946, A330947.

Sequence in context: A378087 A180243 A326728 * A064918 A323076 A286471

Adjacent sequences: A330941 A330942 A330943 * A330945 A330946 A330947

Keyword

nonn,easy

Author

Gus Wiseman, Jan 13 2020

Status

approved