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

2,5

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A349163 A279495 A300409 * A247462 A323172 A327403

Adjacent sequences: A361628 A361629 A361630 * A361632 A361633 A361634

Keyword

nonn,frac

Author

Stefano Spezia, Mar 18 2023

Status

approved