cp's OEIS Frontend

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).

%I A079872 #14 Sep 02 2025 11:01:42
%S A079872 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,
%T A079872 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,
%U A079872 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
%N 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).
%C A079872 a(m) = 0 iff m is a prime power (A000961).
%H A079872 Paolo Xausa, <a href="/A079872/b079872.txt">Table of n, a(n) for n = 1..10000</a>
%F A079872 a(n) = A057427(A079869(n) - n).
%t A079872 A079872[n_] := If[n == 1, 0, Sign[Round[n^(1/#)]^# - n] & [PrimeOmega[n]]];
%t A079872 Array[A079872, 100] (* _Paolo Xausa_, Sep 02 2025 *)
%Y A079872 Cf. A000961, A001222, A057427, A079869.
%K A079872 sign,changed
%O A079872 1,1
%A A079872 _Reinhard Zumkeller_, Jan 13 2003