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.

A055679 Number of distinct prime factors of phi(n!).

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%I A055679 #22 Aug 14 2024 08:35:31
%S A055679 0,0,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,6,6,7,
%T A055679 7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,11,11,11,
%U A055679 11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,13,13,13,13,14,14,14
%N A055679 Number of distinct prime factors of phi(n!).
%C A055679 Number of distinct prime factors of n! and phi(n!) are respectively pi(n) and pi(floor(n/2)).
%H A055679 G. C. Greubel, <a href="/A055679/b055679.txt">Table of n, a(n) for n = 1..5000</a>
%F A055679 a(n) = A001221(A000010(A000142(n))) = A001221(A048855(n)).
%F A055679 a(n) = pi(floor(n/2)).
%t A055679 PrimeNu[EulerPhi[Range[90]!]] (* _Harvey P. Dale_, Sep 27 2011 *)
%o A055679 (PARI) for(n=1,50, print1(omega(eulerphi(n!)), ", ")) \\ _G. C. Greubel_, May 19 2017
%o A055679 (PARI) a(n) = primepi(n\2); \\ _Michel Marcus_, Aug 13 2024
%Y A055679 Cf. A000010, A000142, A000720, A001221, A055718.
%K A055679 nonn,easy
%O A055679 1,6
%A A055679 _Labos Elemer_, Jul 11 2000