login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 


A062402
a(n) = sigma(phi(n)).
75
1, 1, 3, 3, 7, 3, 12, 7, 12, 7, 18, 7, 28, 12, 15, 15, 31, 12, 39, 15, 28, 18, 36, 15, 42, 28, 39, 28, 56, 15, 72, 31, 42, 31, 60, 28, 91, 39, 60, 31, 90, 28, 96, 42, 60, 36, 72, 31, 96, 42, 63, 60, 98, 39, 90, 60, 91, 56, 90, 31, 168, 72, 91, 63, 124, 42, 144, 63, 84, 60, 144
OFFSET
1,3
COMMENTS
Makowski and Schinzel conjectured in 1964 that a(n) = sigma(phi(n)) >= n/2 for all n (B42 of Guy Unsolved Problems...). This has been verified for various classes of numbers and proved to be true in general if it is true for squarefree integers (see Cohen's paper). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002
Atanassov proves the above conjecture. - Charles R Greathouse IV, Dec 06 2016
REFERENCES
Krassimir T. Atanassov, One property of φ and σ functions, Bull. Number Theory Related Topics 13 (1989), pp. 29-37.
A. Makowski and A. Schinzel, On the functions phi(n) and sigma(n), Colloq. Math. 13, 95-99 (1964).
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 13.
LINKS
G. L. Cohen, On a conjecture of Makowski and Schinzel. Colloq. Math. 74, No. 1, 1-8 (1997).
A. Grytczuk, F. Luca and M. Wojtowicz, On a conjecture of Makowski and Schinzel concerning the composition of the arithmetic functions sigma and phi, Colloq. Math. 86, No. 1, 31-36 (2000).
F. Luca and C. Pomerance, On some problems of Makowski-Schinzel and Erdos concerning the arithmetical functions phi and sigma, Colloq. Math. 92, No. 1, 111-130 (2002).
FORMULA
sigma(A062401(x)) = a(sigma(x)) or phi(a(x)) = A062401(phi(x)). - Labos Elemer, Jul 22 2004
EXAMPLE
a(9)= 12 because phi(9)= 6 and sigma(6)= 12.
MAPLE
with(numtheory); A062402:=n->sigma(phi(n)); seq(A062402(k), k=1..100); # Wesley Ivan Hurt, Nov 01 2013
MATHEMATICA
Table[DivisorSigma[1, EulerPhi[n]], {n, 1, 80}] (* Carl Najafi, Aug 16 2011 *)
PROG
(PARI) a(n)=sigma(eulerphi(n));
vector(150, n, a(n))
(Haskell)
a062402 = a000203 . a000010 -- Reinhard Zumkeller, Jan 04 2013
(Python)
from sympy import divisor_sigma, totient
print([divisor_sigma(totient(n)) for n in range(1, 101)]) # Indranil Ghosh, Mar 18 2017
(Magma) [SumOfDivisors(EulerPhi(n)): n in [1..100]] // Marius A. Burtea, Jan 19 2019
KEYWORD
nonn
AUTHOR
Jason Earls, Jul 08 2001
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 22 23:47 EDT 2024. Contains 376140 sequences. (Running on oeis4.)