A173748 Numbers k such that phi(phi(k)) = sigma(rad(k)).

1, 108, 135, 196, 245, 297, 539, 810, 1008, 1176, 1575, 1782, 1917, 3056, 3213, 4464, 6897, 6944, 7560, 8820, 9450, 10017, 11502, 14229, 16632, 16821, 18009, 18336, 19278, 19404, 20320, 24255, 25400, 25823, 27504, 28677, 33250, 33480, 41382

Offset

1,2

Comments

rad(k) is the product of the primes dividing k (A007947), phi(k) is the Euler totient function (A000010), sigma(k) is the sum of divisors of k (A000203).

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.

Links

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

Wacław Sierpiński, Number Of Divisors And Their Sum, Elementary theory of numbers, Warszawa, 1964.

Formula

k such that A000010(A000010(k)) = A000203(A007947(k)).

Example

for n=108,phi(108) = 36,phi(36)=12, rad(108)=6 and sigma(6) = 12

Maple

with(numtheory): for n from 1 to 1000000 do : t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)): if phi(phi(n)) = sigma(t2)then print (n): else fi: od :

Mathematica

Select[Range[50000], EulerPhi[EulerPhi[#]]==DivisorSigma[1, Times@@ FactorInteger[ #][[All, 1]]]&] (* Harvey P. Dale, Aug 21 2016 *)

Prog

(Magma) [1] cat [m:m in [2..42000]|EulerPhi((EulerPhi(m))) eq &+Divisors(&*PrimeDivisors(m))]; // Marius A. Burtea, Jul 10 2019

Crossrefs

Cf. A000010, A000203, A007947.

Sequence in context: A327338 A217541 A070797 * A274118 A046294 A039601

Adjacent sequences: A173745 A173746 A173747 * A173749 A173750 A173751

Keyword

nonn

Author

Michel Lagneau, Feb 23 2010

Status

approved