A361633 a(n) is the denominator of the median of the prime factors of n with repetition.

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

Offset: 2

Author

Stefano Spezia, Mar 18 2023

Keywords

• nonn
• frac

Examples

			a(12) = 1 since 12 = 2*2*3, and the median of the factors is equal to 2/1.
a(36) = 2 since 30 = 2*2*3*3, and the median of the factors is equal to 5/2.
		

Crossrefs

Cf. A001222, A027746, A079879, A323172, A361566, A361631 (without repetition), A361632 (numerator), A361725.

Programs

Mathematica

a[n_]:=Denominator[Median[Flatten[ Table[#[[1]], {#[[2]]}] & /@ FactorInteger[n]]]]; Array[a,88,2]

Formula

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

a(n) = denominator((A079879(n) + A361725(n))/2).

Extensions

Example corrected by Peter Munn, Aug 04 2024