cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A308967 Number of prime factors (with multiplicity) of the numerator A001008 of the harmonic number H(n) = Sum_{k=1..n} 1/k.

This page as a plain text file.
%I A308967 #18 Feb 24 2020 08:17:42
%S A308967 0,1,1,2,1,2,3,1,1,3,2,3,3,2,2,3,2,3,2,2,1,5,2,3,2,1,3,3,3,5,2,3,2,2,
%T A308967 2,5,2,4,2,4,1,4,3,4,3,4,4,3,2,3,3,5,2,3,2,1,3,5,2,4,2,1,4,4,4,6,4,2,
%U A308967 1,4,4,4,3,3,4,4,5,4,1,4,3,3,4,4,3,3,4,5,1,2,1,3,2,2,3,3,3,3,3
%N A308967 Number of prime factors (with multiplicity) of the numerator A001008 of the harmonic number H(n) = Sum_{k=1..n} 1/k.
%H A308967 Amiram Eldar, <a href="/A308967/b308967.txt">Table of n, a(n) for n = 1..325</a>
%F A308967 a(n) = A001222(A001008(n)).
%e A308967 H(1) = 1 = 1/1, the numerator is the empty product, whence a(1) = 0.
%e A308967 H(2) = 1 + 1/2 = 3/2 and H(3) = 3/2 + 1/3 = 11/6, 3 and 11 are prime numbers, whence a(2) = a(3) = 1.
%e A308967 H(4) = 11/6 + 1/4 = 25/12, 25 = 5^2, whence a(4) = 2.
%t A308967 Table[PrimeOmega @ Numerator[HarmonicNumber[n]], {n, 30}] (* _Amiram Eldar_, Feb 24 2020 *)
%o A308967 (PARI) a(n)=bigomega(A001008(n))
%Y A308967 Cf. A001008, A001222.
%K A308967 nonn
%O A308967 1,4
%A A308967 _M. F. Hasler_, Jul 03 2019