A079872 a(1)=0, a(n) = signum(round(n^(1/Omega(n)))^Omega(n) - n), where Omega(n) is the total number of prime factors of n (A001222).

0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 1, 1, 1, -1, 0, -1, -1, 1, 0, -1, 0, 1, 1, 1, 0, -1, 0, 1, -1, 1, 0, 1, -1, 1, 1, 1, 0, 1, 0, 1, 1, 0, -1, -1, 0, -1, -1, -1, 0, -1, 0, 1, -1, -1, 1, -1, 0, -1, 0, -1, 0, -1, -1, -1, -1, -1, 0, -1, 1, 1, 1, 1, 1, -1

Offset: 1

Author

Reinhard Zumkeller, Jan 13 2003

Keywords

• sign
• changed

Comments

a(m) = 0 iff m is a prime power (A000961).

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000961, A001222, A057427, A079869.

Programs

Mathematica

A079872[n_] := If[n == 1, 0, Sign[Round[n^(1/#)]^# - n] & [PrimeOmega[n]]];
Array[A079872, 100] (* Paolo Xausa, Sep 02 2025 *)

Formula

a(n) = A057427(A079869(n) - n).