A361631 a(n) is the denominator of the median of the distinct prime factors of n.

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, 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, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1

Offset: 2

Author

Stefano Spezia, Mar 18 2023

Keywords

• nonn
• frac

Examples

			a(12) = 2 since the distinct prime factors of 12 are 2 and 3, of median equal to 5/2.
a(30) = 1 since the distinct prime factors of 30 are 2, 3, and 5, of median equal to 3.
		

Links

• Winston de Greef, Table of n, a(n) for n = 2..10000

Crossrefs

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

Programs

Mathematica

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

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

Formula

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