A259651 - OEIS

A259651

Number of distinct prime factors of the n-th pentagonal number (A000326).

0, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 4, 3, 3, 2, 4, 4, 2, 3, 2, 3, 3, 2, 4, 4, 2, 2, 4, 4, 2, 3, 4, 3, 4, 2, 3, 4, 3, 3, 4, 2, 3, 3, 3, 4, 3, 4, 3, 4, 2, 3, 4, 3, 4, 3, 3, 3, 2, 3, 3, 4, 3, 2

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OFFSET

1,3

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A001221(A000326(n)).

EXAMPLE

a(3) = 2 because A000326(3) = 12 = 2^2 * 3.

MATHEMATICA

a[n_] := PrimeNu[n*(3*n-1)/2]; Array[a, 100] (* Amiram Eldar, Sep 15 2024 *)

PrimeNu[PolygonalNumber[5, Range[100]]] (* Harvey P. Dale, Aug 22 2025 *)