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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

Table of n, a(n) for n=1..46.

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.)