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.

A145190 Numbers k such that phi(1)*phi(2)*...*phi(k) / k is an integer, where phi(k) is the totient function (A000010).

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%I A145190 #23 Jul 16 2022 07:14:24
%S A145190 1,4,8,9,12,15,16,18,20,24,25,27,30,32,33,35,36,40,42,44,45,48,49,50,
%T A145190 54,55,56,60,63,64,65,66,69,70,72,75,77,78,80,81,84,87,88,90,91,92,96,
%U A145190 98,99,100,104,105,108,110,112,115,116,117,119,120,121,123
%N A145190 Numbers k such that phi(1)*phi(2)*...*phi(k) / k is an integer, where phi(k) is the totient function (A000010).
%H A145190 Amiram Eldar, <a href="/A145190/b145190.txt">Table of n, a(n) for n = 1..10000</a>
%t A145190 Select[Range[200], IntegerQ[Product[EulerPhi[i], {i, 1, #}]/#] &] (* _Carl Najafi_, Aug 19 2011 *)
%t A145190 nn=150;With[{ep=Rest[FoldList[Times,1,EulerPhi[Range[nn]]]]}, Flatten[ Position[Table[ep[[i]]/i,{i,nn}],_?IntegerQ]]] (* _Harvey P. Dale_, May 12 2012 *) (* this program is more than 200 times faster than the first Mathematica program above *)
%o A145190 (PARI) isok(n)=prod(k=1,n,eulerphi(k))%n==0 \\ _Anders Hellström_, Aug 22 2015
%Y A145190 Cf. A000010, A048290, A144857.
%K A145190 easy,nonn
%O A145190 1,2
%A A145190 _Ctibor O. Zizka_, Oct 03 2008
%E A145190 More terms from _Carl Najafi_, Aug 19 2011