A173337 Numbers k>1 such that phi(phi(k))= sigma(sopf(k)).

40, 50, 54, 171, 195, 231, 330, 377, 387, 518, 638, 742, 745, 888, 1057, 1141, 1397, 1561, 1788, 2422, 2682, 2763, 3206, 3357, 3805, 4037, 4344, 4382, 4915, 5093, 5138, 5391, 5558, 5951, 6147, 8063, 8952, 9132, 9422, 10109, 10968, 11796, 12287, 12481

Offset

1,1

Comments

sopf(k) is the sum of the distinct primes dividing k (without repetition): A008472), phi(k) is the Euler totient function (A000010), sigma(k) is the sum of divisors of k (A000203).

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Formula

k such that A010554(k)= sigma(A008472(k)).

Example

40 is in the sequence because phi(40)= 16, phi(16) = 8, sopf(40) = 7 and sigma(7) = 8;
171 is in the sequence because phi(171) = 108, phi(108) = 36, sopf(171) = 22 and sigma(22) = 36.

Maple

with(numtheory) :
A008472 := proc(n)
        add(p, p = factorset(n):
end proc:
isA173337 := proc(n)
        phi(phi(n)) = sigma(A008472(n)) ;
end proc:
for n from 1 do
        if isA173337(n) then printf("%d, ", n) ; fi;
end do: # R. J. Mathar, Jul 06 2012

Mathematica

sopf[n_] := Plus @@ (First@# & /@ FactorInteger[n]); Select[Range[2, 13000], EulerPhi[EulerPhi[#]] == DivisorSigma[1, sopf[#]] &] (* Amiram Eldar, Jul 09 2019 *)
Select[Range[2, 15000], DivisorSigma[1, Total[FactorInteger[#][[All, 1]]]] == EulerPhi[ EulerPhi[#]]&] (* Harvey P. Dale, Apr 05 2020 *)

Prog

(PARI) isok(n) = (n>1) && eulerphi(eulerphi(n)) == sigma(vecsum(factor(n)[, 1])); \\ Michel Marcus, Jul 10 2019

Crossrefs

Cf. A000010, A000203, A010554, A008472.

Sequence in context: A062909 A167327 A216305 * A167311 A039523 A217729

Adjacent sequences: A173334 A173335 A173336 * A173338 A173339 A173340

Keyword

nonn

Author

Michel Lagneau, Feb 16 2010

Extensions

Definition clarified by N. J. A. Sloane, Apr 05 2020

Status

approved