A361725 a(n) is the largest of two middle prime factors of n if the number of primes divisors counted with multiplicity (A001222(n)) is even, otherwise is the middle prime factor of n.

2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 2, 13, 7, 5, 2, 17, 3, 19, 2, 7, 11, 23, 2, 5, 13, 3, 2, 29, 3, 31, 2, 11, 17, 7, 3, 37, 19, 13, 2, 41, 3, 43, 2, 3, 23, 47, 2, 7, 5, 17, 2, 53, 3, 11, 2, 19, 29, 59, 3, 61, 31, 3, 2, 13, 3, 67, 2, 23, 5, 71, 2, 73, 37, 5, 2, 11, 3

Offset

2,1

Links

Table of n, a(n) for n=2..78.

Formula

a(n) = A027746(n, floor(A001222(n)/2) + 1).

a(n) = 2*A361632(n)/A361633(n) - A079879(n) if A001222(n) is even.

a(n) = A361632(n) if A001222(n) is odd.

Example

a(30) = a(2*3*5) = 3; a(60) = a(2*2*3*5) = 3; a(72) = a(2*2*2*3*3) = 2.

Mathematica

f[n_] := Block[{p = Flatten[Table[#1, {#2}] & @@@ FactorInteger@ n], len}, len = Length@ p; If[OddQ@ len, p[[(1 + len)/2]], p[[len/2+1]]]]; Table[f@ n, {n, 2, 78}] (* After Michael De Vlieger in A079879 *)

Crossrefs

Cf. A001222, A027746, A079879, A361632, A361633.

Sequence in context: A286516 A273289 A365521 * A356840 A346152 A090662

Adjacent sequences: A361722 A361723 A361724 * A361726 A361727 A361728

Keyword

nonn

Author

Stefano Spezia, Mar 22 2023

Status

approved