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.

A173326 Numbers k such that phi(tau(k)) = sopf(k).

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%I A173326 #30 Apr 01 2019 03:01:21
%S A173326 4,8,32,1344,2016,2025,2376,3375,3528,4032,4224,4704,4752,5292,5376,
%T A173326 5625,6084,6804,7128,9408,9504,10125,10206,10935,12100,12348,12672,
%U A173326 16875,16896,20412,21384,23814,26136,28512,29952,30375,31944,32832,42768,46464,48114
%N A173326 Numbers k such that phi(tau(k)) = sopf(k).
%H A173326 Donovan Johnson, <a href="/A173326/b173326.txt">Table of n, a(n) for n = 1..1000</a>
%H A173326 A. Bogomolny, <a href="http://www.cut-the-knot.org/blue/Euler.shtml">Euler Function and Theorem</a>
%H A173326 P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s2-19.1.75">Divisors of numbers and their continuations in the theory of partitions</a>, Proc. London Math. Soc., 19 (1919), 75-113.
%H A173326 W. Sierpinski, <a href="http://matwbn.icm.edu.pl/ksiazki/mon/mon42/mon4204.pdf">Number Of Divisors And Their Sum</a>
%F A173326 {k: A163109(k) = A008472(k)}.
%e A173326 4 is in the sequence because tau(4) = 3, phi(3) = 2 and sopf(4) = 2.
%e A173326 8 is in the sequence because tau(8) = 4, phi(4) = 2 and sopf(8) = 2.
%p A173326 A008472 := proc(n) add(p,p= numtheory[factorset](n)) ; end proc:
%p A173326 A163109 := proc(n) numtheory[phi](numtheory[tau](n)) ; end proc:
%p A173326 for n from 1 to 40000 do if A008472(n) = A163109(n) then printf("%d,",n); end if; end do: # _R. J. Mathar_, Sep 02 2011
%t A173326 Select[Range[2,50000],EulerPhi[DivisorSigma[0,#]]==Total[ Transpose[ FactorInteger[#]][[1]]]&] (* _Harvey P. Dale_, Nov 15 2013 *)
%Y A173326 Cf. A000005 (tau), A000010 (phi), A008472 (sopf).
%Y A173326 Cf. A173320, A062069, A001414, A001222.
%K A173326 nonn
%O A173326 1,1
%A A173326 _Michel Lagneau_, Feb 16 2010
%E A173326 Corrected and edited by _Michel Lagneau_, Apr 25 2010