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A173334
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Numbers n such that tau(phi(n))= phi(sum-of-prime-divisors(n))
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0
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2, 3, 15, 18, 24, 28, 30, 33, 39, 50, 52, 55, 80, 132, 133, 152, 169, 186, 187, 190, 195, 207, 215, 217, 222, 230, 238, 247, 261, 266, 305, 319, 333, 340, 352, 369, 371, 414, 481, 484, 494, 496, 497, 506, 516, 522, 559, 574, 580, 611, 644, 646, 660, 671, 689
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OFFSET
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1,1
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COMMENTS
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Numbers n such that A000005(A000010(n)) = A000010(A008472(n)).
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..55.
P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., 19 (1921), 75-113.
W. Sierpinski, Number Of Divisors And Their Sum, Monogr. Matemat. 42 (1964) chapter IV
Anonymous, Euler's totient function, Wikipedia
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FORMULA
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{n : A062821(n)= phi(A008472(n))}.
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EXAMPLE
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For n=15, tau(phi(15)) = tau(8)=4 equals phi(A008472(15))=phi(8) = 4, which adds 15 to the sequence.
For n=18, tau(phi(18)) = tau(6) =4 equals phi(A008472(18)) = phi(5) = 4, which adds 18 to the sequence.
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MAPLE
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with(numtheory): for n from 1 to 1800 do : t1:= ifactors(n)[2] : t2 :=sum(t1[i][1], i=1..nops(t1)):if tau(phi(n)) = phi(t2) then print (n): else fi : od :
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MATHEMATICA
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Select[Range[2, 700], DivisorSigma[0, EulerPhi[#]] == EulerPhi[Total[FactorInteger[#][[All, 1]]]] &]
(* From Jean-François Alcover, May 19 2011 *)
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CROSSREFS
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Sequence in context: A088030 A101047 A066491 * A101507 A047176 A037175
Adjacent sequences: A173331 A173332 A173333 * A173335 A173336 A173337
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KEYWORD
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nonn
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AUTHOR
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Michel Lagneau, Feb 16 2010
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EXTENSIONS
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Removed sopf acronym. Updated references and links - R. J. Mathar, Mar 10 2010
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STATUS
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approved
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