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
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
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 :
MATHEMATICA
sopf[n_] := Plus @@ (First@# & /@ FactorInteger[n]); Select[Range[2, 5100], DivisorSigma[0, EulerPhi[#]] == DivisorSigma[1, sopf[#]] &] (* Amiram Eldar, Jul 09 2019 *)
PROG
(Magma) [m:m in [2..5100]|#Divisors(EulerPhi(m)) eq &+Divisors(&+PrimeDivisors(m))]; // Marius A. Burtea, Jul 10 2019
(PARI) isok(n) = (n>1) && numdiv(eulerphi(n)) == sigma(vecsum(factor(n)[, 1])); \\ Michel Marcus, Jul 10 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 16 2010
EXTENSIONS
Corrected and edited by Michel Lagneau, Apr 25 2010
Edited by D. S. McNeil, Nov 20 2010
STATUS
approved