OFFSET
1,1
COMMENTS
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..10000
A. Bogomolny, Euler Function and Theorem
P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., 19 (1919), 75-113.
Wacław Sierpiński, Number Of Divisors And Their Sum, Elementary theory of numbers, Warszawa, 1964.
Wikipedia, Euler's totient function
EXAMPLE
4 is in the sequence because phi(4) = 2, tau(2)=2 and sopf(4)=2 ;
45 is in the sequence because phi(45) = 24, tau(24)=8 and sopf(45)=8.
MAPLE
for n from 1 to 150000 do : t1:= ifactors(n)[2] : t2 :=sum(t1[i][1], i=1..nops(t1)):if tau(phi(n)) = t2 then print (n): else fi : od :
MATHEMATICA
tpsQ[n_]:=DivisorSigma[0, EulerPhi[n]]==Total[Transpose[FactorInteger[n]][[1]]]; Select[Range[5000], tpsQ] (* Harvey P. Dale, Apr 10 2013 *)
PROG
(PARI) sopf(n)=my(f=factor(n)[1, ]); sum(i=1, #f, f[i])
is(n)=numdiv(eulerphi(n))==sopf(n) \\ Charles R Greathouse IV, May 20 2013
(Magma) [ m:m in [2..5100]|#Divisors(EulerPhi(m)) eq &+PrimeDivisors(m)]; // Marius A. Burtea, Jul 10 2019
CROSSREFS
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