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.

A328275 Numbers m such that phi(m) = rad(m)^4, where phi is the Euler totient function (A000010) and rad is the squarefree kernel function (A007947).

This page as a plain text file.
%I A328275 #10 Nov 23 2019 23:12:54
%S A328275 1,32,3888,25000,2839714,3037500,10890936,120298932,402627500,
%T A328275 534837384,7489147356,8508543750,48919241250,111945866022,
%U A328275 336977358354,417841706250,553904623764,1498168652148,2627525125250,2761526809032,2898701538750,7978057537338,16548448068126,20978349935382
%N A328275 Numbers m such that phi(m) = rad(m)^4, where phi is the Euler totient function (A000010) and rad is the squarefree kernel function (A007947).
%C A328275 De Koninck et al. showed that there are 85 terms in this sequence, yet a(6) = 3037500 was missing in their paper. With a(6), it was verified numerically that the first 38 terms (terms below 10^18) are correct.
%H A328275 Jean-Marie De Koninck, Florian Luca and A. Sankaranarayanan, <a href="https://projecteuclid.org/euclid.rmjm/1181069489">Positive integers whose Euler function is a power of their kernel function</a>, Rocky Mountain Journal of Mathematics, Vol. 36, No. 1 (2006), pp. 81-96, <a href="https://www.jeanmariedekoninck.mat.ulaval.ca/fileadmin/jmdk/Documents/Publications/2006_positive_integers_whose_euler_function_is_a_power_of_their_kernel_function.pdf">alternative link</a>.
%e A328275 32 is in the sequence since phi(32) = 16, rad(32) = 2 and 16 = 2^4.
%t A328275 rad[n_] := Times @@ First /@ FactorInteger[n]; aQ[n_] := EulerPhi[n] == rad[n]^4; Select[Range[3*10^6], aQ]
%o A328275 (PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
%o A328275 isok(m) = eulerphi(m) == rad(m)^4; \\ _Michel Marcus_, Oct 15 2019
%Y A328275 Cf. A000010, A007947, A105261, A211413, A328274, A328276.
%K A328275 nonn,fini
%O A328275 1,2
%A A328275 _Amiram Eldar_, Oct 10 2019
%E A328275 a(6) = 3037500 from _Marius A. Burtea_, Oct 11 2019