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

99, 168, 187, 493, 637, 780, 943, 1273, 1537, 1836, 2183, 2225, 2976, 3103, 3589, 4183, 5353, 5928, 6201, 6468, 6667, 8881, 9553, 9727, 13393, 13888, 14453, 15397, 17587, 19897, 24253, 24883, 30883, 33667, 36259, 36853, 37523, 43657, 45901

Offset: 1

Author

Robert G. Wilson v, Jun 30 2000

Keywords

• easy
• nonn

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000010, A000203, A068422.

Programs

Maple

filter:= proc(n) uses numtheory;
  if isprime(n) then return false fi;
  type(sigma(n)/(n-phi(n)), integer)
end proc:
select(filter, [seq(seq(4*i+j,j=[0,1,3]),i=1..20000)]); # Robert Israel, May 03 2019

Mathematica

Do[ If[ !PrimeQ[ n ], If[ Mod[ n, 4 ] != 2, If[ Mod[ DivisorSigma[ 1, n ], n-EulerPhi[ n ] ] == 0, Print[ n ] ] ] ], {n, 2, 50000} ]

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