cp's OEIS Frontend

A381954 The maximum exponent in the prime factorization of n that is coprime to n, or 0 if no such exponent exists.

%I A381954 #6 Mar 12 2025 08:24:40
%S A381954 0,1,1,0,1,1,1,3,2,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,2,1,0,1,1,1,1,5,1,1,
%T A381954 1,0,1,1,1,3,1,1,1,1,2,1,1,1,2,1,1,1,1,1,1,3,1,1,1,1,1,1,2,0,1,1,1,1,
%U A381954 1,1,1,0,1,1,2,1,1,1,1,1,4,1,1,1,1,1,1
%N A381954 The maximum exponent in the prime factorization of n that is coprime to n, or 0 if no such exponent exists.
%C A381954 The sums of the first 10^k terms, for k = 1, 2, ..., are 11, 118, 1250, 12648, 126955, 1271426, 12720020, 127218134, 1272236949, 12722547575, .... . Apparently, the asymptotic mean of this sequence equals 1.2722... .
%H A381954 Amiram Eldar, <a href="/A381954/b381954.txt">Table of n, a(n) for n = 1..10000</a>
%e A381954 a(2) = 1 since 2 = 2^1 and 1 is coprime to 2.
%e A381954 a(4) = 0 since 4 = 2^2 and the exponent 2 is not coprime to 4.
%e A381954 a(12) = 1 since 12 = 2^2 * 3^1, the exponent 2 is not coprime to 12, and the exponent 1 is coprime to 12.
%t A381954 a[n_] := If[(s = Select[FactorInteger[n][[;; , 2]], CoprimeQ[#, n] &]) != {}, Max[s], 0]; a[1] = 0; Array[a, 100]
%o A381954 (PARI) a(n) = {my(e = factor(n)[, 2], s = select(x -> if(gcd(x, n) == 1, x, 0), e)); if(#s == 0, 0, vecmax(s));}
%Y A381954 Cf. A051903, A381952.
%K A381954 nonn,easy
%O A381954 1,8
%A A381954 _Amiram Eldar_, Mar 11 2025