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.

A114063 Numbers k such that phi(k) = tau(k)^4, where tau(k) = A000005(k).

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%I A114063 #35 Jun 02 2024 08:51:08
%S A114063 1,17,514,8738,32301,33003,36351,41504,42292,43852,51860,62226,549117,
%T A114063 561051,571311,599067,617967,629811,634005,657495,673184,674505,
%U A114063 683168,701024,705568,718964,722684,732628,745484,759772,774368
%N A114063 Numbers k such that phi(k) = tau(k)^4, where tau(k) = A000005(k).
%C A114063 For all large enough k, we have tau(k) < k^(1/5) and phi(k) > k^(4/5). Hence, tau(k)^4 < k^(4/5) < phi(k), implying that this sequence is finite. - _Max Alekseyev_, Mar 10 2016
%C A114063 Sequence is composed of 94030 terms. - _Max Alekseyev_, Jun 01 2024
%H A114063 Max Alekseyev, <a href="/A114063/b114063.txt">Table of n, a(n) for n = 1..94030</a> (first 660 terms from Enrique Pérez Herrero; terms 661..7000 from Giovanni Resta)
%e A114063 phi(33003) = 20736. tau(33003) = 12, 20736 = 12^4.
%e A114063 a(2) = A107655(4) = 17.
%t A114063 Select[Range[10^6], EulerPhi[#] == DivisorSigma[0, #]^4 &] (* _Paolo Xausa_, May 31 2024 *)
%o A114063 (PARI) isok(n) = eulerphi(n) == numdiv(n)^4; \\ _Michel Marcus_, Jan 22 2014
%Y A114063 Subsequence of A078164.
%Y A114063 Cf. A020488, A062516, A063469, A063470, A107655, A112954, A112955, A175667, A068560, A068559.
%K A114063 fini,full,nonn
%O A114063 1,2
%A A114063 _Giovanni Resta_, Feb 13 2006