A361631 - OEIS

%I #14 Mar 23 2023 23:09:03

%S 1,1,1,1,2,1,1,1,2,1,2,1,2,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,2,1,

%T 2,1,2,1,2,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,2,1,1,1,1,1,2,1,

%U 1,1,2,1,2,1,2,1,1,1,2,1,2,1,1,1,2,1,2,1

%N a(n) is the denominator of the median of the distinct prime factors of n.

%H Winston de Greef, <a href="/A361631/b361631.txt">Table of n, a(n) for n = 2..10000</a>

%F For p a prime, a(p^k) = 1.

%e a(12) = 2 since the distinct prime factors of 12 are 2 and 3, of median equal to 5/2.

%e a(30) = 1 since the distinct prime factors of 30 are 2, 3, and 5, of median equal to 3.

%t a[n_]:=Denominator[Median[FactorInteger[n][[All, 1]]]]; Array[a,88,2]

%o (PARI) a(n)=my(f=factor(n)[,1]~, i=length(f)); denominator(if(i%2, f[i\2+1], (f[i/2]+f[i/2+1])/2)) \\ _Winston de Greef_, Mar 23 2023

%Y Cf. A001221, A027748, A323172, A361566, A361630 (numerator), A361633 (with multiplicity).

%K nonn,frac

%O 2,5

%A _Stefano Spezia_, Mar 18 2023