A217842 - OEIS

%I #16 Nov 15 2024 07:00:01

%S 2,72,1,4800,1,15876,1,3456000,1,242,1,300500928,1,1,1,2130739200,1,

%T 1052676,1,119790000,1,1058,1,531598161669120000,1,1,1,1682,1,1922,1,

%U 20864198246400,1,1,1,1159208596538496,1,1,1,265804426800000000,1,17757796,1

%N Product of the numbers p such that phi(p) = n, where phi is Euler's totient function.

%C It appears that all terms greater than 1 are distinct. This is true for all n <= 10^6.

%H T. D. Noe, <a href="/A217842/b217842.txt">Table of n, a(n) for n = 1..1000</a>

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).

%H 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.

%t Needs["CNT`"]; Table[Times @@ PhiInverse[n], {n, 100}]

%o (PARI) a(n) = vecprod(invphi(n)); \\ _Amiram Eldar_, Nov 15 2024, using _Max Alekseyev_'s invphi.gp

%Y Cf. A002181 (smallest inverse), A006511 (largest inverse), A215240 (sum of inverses).

%Y Cf. A032447 (inverse of phi).

%K nonn,changed

%O 1,1

%A _T. D. Noe_, Oct 12 2012