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A055164 (n - phi(n)) | sigma(n) for composite n not congruent to 2 (mod 4).

%I A055164 #21 Jun 22 2025 03:58:55
%S A055164 99,168,187,493,637,780,943,1273,1537,1836,2183,2225,2976,3103,3589,
%T A055164 4183,5353,5928,6201,6468,6667,8881,9553,9727,13393,13888,14453,15397,
%U A055164 17587,19897,24253,24883,30883,33667,36259,36853,37523,43657,45901
%N A055164 (n - phi(n)) | sigma(n) for composite n not congruent to 2 (mod 4).
%C A055164 Let p be an odd prime.  If d > p+1 is a divisor of p^2 - p - 2 such that d+1-p is prime, then p*(d+1-p) is in the sequence. - _Robert Israel_, May 03 2019
%H A055164 Robert Israel, <a href="/A055164/b055164.txt">Table of n, a(n) for n = 1..500</a>
%p A055164 filter:= proc(n) uses numtheory;
%p A055164   if isprime(n) then return false fi;
%p A055164   type(sigma(n)/(n-phi(n)), integer)
%p A055164 end proc:
%p A055164 select(filter, [seq(seq(4*i+j,j=[0,1,3]),i=1..20000)]); # _Robert Israel_, May 03 2019
%t A055164 Do[ If[ !PrimeQ[ n ], If[ Mod[ n, 4 ] != 2, If[ Mod[ DivisorSigma[ 1, n ], n-EulerPhi[ n ] ] == 0, Print[ n ] ] ] ], {n, 2, 50000} ]
%o A055164 (Sage) [n for n in (1..50000) if not mod(n, 4)==2 and not is_prime(n) and mod(sigma(n), n - euler_phi(n))==0] # _G. C. Greubel_, May 03 2019
%Y A055164 Cf. A000010, A000203, A068422.
%K A055164 easy,nonn
%O A055164 1,1
%A A055164 _Robert G. Wilson v_, Jun 30 2000