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 A173618 Numbers k such that tau(phi(k)) = rad(k). 1
 1, 4, 36, 54, 96, 200, 448, 1280, 2700, 4500, 5103, 9720, 11264, 14112, 14580, 17280, 26624, 32928, 48000, 54432, 71442, 75000, 81648, 152064, 184320, 187500, 258048, 307200, 350000, 637875, 1250235, 1344560, 1557504, 2044416, 2187500, 2367488, 3234816 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS rad(k) is the product of the primes dividing k (A007947), tau(k) is the number of divisors of k (A000005), phi(k) is the Euler totient function (A000010). 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..100 W. Sierpinski, Number Of Divisors And Their Sum Wikipedia, Euler's totient function FORMULA k such that A062821(k) = A007947(k). EXAMPLE phi(4) = 2, tau(2) = 2 and rad(4) = 2 phi(36) = 12, tau(12) = 6 and rad(36) = 6 MAPLE with(numtheory):for n from 1 to 1000000 do : t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)): if tau(phi(n))= t2 then print (n): else fi: od : MATHEMATICA rad[n_] := Times @@ (First@# & /@ FactorInteger[n]); Select[Range[10^5], DivisorSigma[0, EulerPhi[#]] == rad[#] &] (* Amiram Eldar, Jul 09 2019*) PROG (PARI) isok(k) = numdiv(eulerphi(k)) == factorback(factorint(k)[, 1]); \\ Michel Marcus, Jul 09 2019 CROSSREFS Cf. A000005, A000010, A062069, A062821, A007947, A173326. Sequence in context: A219247 A224094 A280934 * A091722 A053939 A167632 Adjacent sequences:  A173615 A173616 A173617 * A173619 A173620 A173621 KEYWORD nonn,changed AUTHOR Michel Lagneau, Feb 22 2010 EXTENSIONS a(30)-a(37) from Donovan Johnson, Jul 27 2011 STATUS approved

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Last modified July 22 14:33 EDT 2019. Contains 325222 sequences. (Running on oeis4.)