A058979 - OEIS

%I #14 Dec 10 2024 18:00:59

%S 4,5,6,6,5,10,2,7,8,9,3,11,2,3,9,8,0,17,0,10,6,6,3,17,4,3,9,6,3,17,0,

%T 9,7,2,3,21,2,0,7,12,3,12,2,8,10,4,0,21,2,8,3,4,3,19,5,8,2,6,0,31,0,0,

%U 9,10,3,10,2,5,9,8,0,28,2,3,5,0,0,16,2,16,8,4,3,18,0,3,6,12,3,25,0,5,2,0

%N Number of numbers m such that phi(m) = 4n.

%C Size of invphi(4n) solution-set.

%H Amiram Eldar, <a href="/A058979/b058979.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A014197(4*n). - _Amiram Eldar_, Dec 10 2024

%e For n = 12: 4*n = 48, invphi(48) has 11 solutions: {65,104,105,112,130,140,144,156,168,180,210}, so a(12) = 11.

%e The value of the "nops(invphi(4k))" number seems to take any integer except 1.

%p with(numtheory): [seq(nops(invphi(4*k)),k=1...256)];

%o (PARI) a(n) = invphiNum(4*n); \\ _Amiram Eldar_, Dec 10 2024, using _Max Alekseyev_'s invphi.gp

%Y Cf. A000010, A005277, A014197.

%K nonn

%O 1,1

%A _Labos Elemer_, Jan 15 2001

%E Offset corrected by _Sean A. Irvine_, Sep 08 2022