A361630 -id:A361630 - cp's OEIS frontend

A361632 a(n) is the numerator of the median of the prime factors of n with repetition.

2, 3, 2, 5, 5, 7, 2, 3, 7, 11, 2, 13, 9, 4, 2, 17, 3, 19, 2, 5, 13, 23, 2, 5, 15, 3, 2, 29, 3, 31, 2, 7, 19, 6, 5, 37, 21, 8, 2, 41, 3, 43, 2, 3, 25, 47, 2, 7, 5, 10, 2, 53, 3, 8, 2, 11, 31, 59, 5, 61, 33, 3, 2, 9, 3, 67, 2, 13, 5, 71, 2, 73, 39, 5, 2, 9, 3, 79

Offset: 2

Stefano Spezia, Mar 18 2023

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

Cf. A001222, A027746, A079879, A323171, A361565, A361630 (without repetition), A361633 (denominator), A361725.

a[n_]:=Numerator[Median[Flatten[Table[#[[1]], {#[[2]]}] & /@ FactorInteger[n]]]]; Array[a,78,2]

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

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

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

Original entry on oeis.org

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

Stefano Spezia, Mar 18 2023

			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.

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

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

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

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

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

cp's OEIS Frontend

A361632 a(n) is the numerator of the median of the prime factors of n with repetition.

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