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

2,1

Links

Table of n, a(n) for n=2..79.

Formula

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

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A141346 A095402 A086294 * A075860 A361630 A323171

Adjacent sequences: A361629 A361630 A361631 * A361633 A361634 A361635

Keyword

nonn,frac

Author

Stefano Spezia, Mar 18 2023

Status

approved