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 A173748 Numbers k such that phi(phi(k)) = sigma(rad(k)). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 22 04:01 EDT 2023. Contains 365503 sequences. (Running on oeis4.)