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

1,1

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

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 ]! = 0, If[ Mod[ DivisorSigma[ 1, n ], n-EulerPhi[ n ] ] == 0, Print[ n ] ] ], {n, 1, 5000} ]

Prog

(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

Crossrefs

Cf. A000010, A000203, A068422.

Sequence in context: A325881 A185498 A126230 * A075815 A075814 A320707

Adjacent sequences: A055161 A055162 A055163 * A055165 A055166 A055167

Keyword

easy,nonn

Author

Robert G. Wilson v, Jun 30 2000

Status

approved