A066934 - OEIS

%I #19 Dec 10 2024 11:59:35

%S 8,12,32,48,75,108,110,125,128,170,192,208,230,280,290,312,363,368,

%T 374,405,410,420,470,506,530,552,590,638,680,684,688,702,710,782,830,

%U 848,867,890,902,935,980,986,1008,1010,1020,1032,1034,1044,1070,1080,1088

%N Numbers k such that phi(k)==1 (mod bigomega(k)) where phi(n)=A000010(n) is the Euler totient function and bigomega(n)=A001222(n) is the number of prime divisors of n (counted with multiplicity).

%C Trivially, all terms are composite.

%H Harry J. Smith, <a href="/A066934/b066934.txt">Table of n, a(n) for n = 1..1000</a>

%t bigomega[n_] := Plus@@Last/@FactorInteger[n]; Select[Range[2, 1100], !PrimeQ[ # ]&&Mod[EulerPhi[ # ]-1, bigomega[ # ]]==0&]

%t Select[Range[1100],CompositeQ[#]&&Mod[EulerPhi[#],PrimeOmega[#]]==1&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 14 2018 *)

%o (PARI) isok(k) = { k > 1 && eulerphi(k) % bigomega(k) == 1 } \\ _Harry J. Smith_, Apr 08 2010

%K nonn

%O 1,1

%A _Benoit Cloitre_, Jan 24 2002

%E Edited by _Dean Hickerson_, Jan 27 2002

%E Comment corrected by _Harry J. Smith_, Apr 08 2010