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 A173336 Numbers n such that tau(phi(n))= sigma(sopf(n)). 0
 8, 9, 25, 36, 49, 54, 96, 100, 320, 441, 495, 704, 891, 1029, 1080, 1089, 1260, 1331, 1386, 1400, 1617, 1701, 1750, 1815, 1848, 1950, 1960, 2079, 2541, 2574, 2704, 2850, 2880, 3000, 3360, 3430, 3510, 3861, 4125, 4275, 4680, 4704, 4719, 4800, 5070, 5096 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS tau(n) is the number of divisors of n (A000005); phi(n) is the Euler totient function (A000010); sigma(n) the sum of divisors of n (A000203); and sopf(n) is the sum of the distinct primes dividing n without repetition (A008472). REFERENCES P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., 19 (1919), 75-113. 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 W. Sierpinski, Number Of Divisors And Their Sum Wikipedia, Euler's totient function FORMULA n such that A062821 (n)= sigma(A008472(n)) EXAMPLE 8 is in the sequence because phi(8) = 4, tau(4)=3, sopf(8)=2 and sigma(2) = 3 ; 9 is in the sequence because phi(9) = 6, tau(6)=4, sopf(9)=3 and sigma(3) = 4. MAPLE with(numtheory): for n from 1 to 18000 do : t1:= ifactors(n)[2] : t2 :=sum(t1[i][1], i=1..nops(t1)):if tau(phi(n)) = sigma(t2) then print (n): else fi : od : CROSSREFS Cf. A001157, A001158, A001160, A001065, A002192 Sequence in context: A130100 A226230 A258400 * A277925 A173745 A305828 Adjacent sequences:  A173333 A173334 A173335 * A173337 A173338 A173339 KEYWORD nonn AUTHOR Michel Lagneau, Feb 16 2010 EXTENSIONS Added punctuation to the examples. Corrected and edited by Michel Lagneau, Apr 25 2010 Edited by D. S. McNeil, Nov 20 2010 STATUS approved

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Last modified February 17 10:59 EST 2019. Contains 320219 sequences. (Running on oeis4.)