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.

A378506 The number of solutions to the equation phi(phi(x)) = n, where phi is the Euler totient function.

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%I A378506 #8 Nov 30 2024 06:26:20
%S A378506 5,8,0,13,0,4,0,23,0,2,0,14,0,0,0,36,0,2,0,5,0,2,0,32,0,0,0,2,0,0,0,
%T A378506 54,0,0,0,11,0,0,0,23,0,0,0,5,0,0,0,66,0,0,0,2,0,4,0,3,0,0,0,2,0,0,0,
%U A378506 78,0,0,0,0,0,0,0,38,0,0,0,0,0,0,0,41,0,2,0,6
%N A378506 The number of solutions to the equation phi(phi(x)) = n, where phi is the Euler totient function.
%H A378506 Amiram Eldar, <a href="/A378506/b378506.txt">Table of n, a(n) for n = 1..10000</a>
%H A378506 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%H A378506 David M. Bressoud, <a href="https://www.davidbressoud.org/books-videos">A Course in Computational Number Theory (web page)</a>, <a href="https://drive.google.com/file/d/1UMesJ93mpdCabQvETMqOBH8eCR4JWA6X/view?usp=sharing">CNT.m</a>, Computational Number Theory Mathematica package.
%F A378506 a(n) > 0 if and only if n is in A378508.
%t A378506 a[n_] := Sum[PhiMultiplicity[i], {i, PhiInverse[n]}]; Array[a, 100] (* using David M. Bressoud's CNT.m *)
%o A378506 (PARI) a(n) = vecsum(apply(x -> invphiNum(x), invphi(n))); \\ using _Max Alekseyev_'s invphi.gp
%Y A378506 Cf. A000010, A010554, A014197, A378507, A378508.
%K A378506 nonn,easy
%O A378506 1,1
%A A378506 _Amiram Eldar_, Nov 29 2024