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%I A062402 #47 Sep 08 2022 08:45:03
%S A062402 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,
%T A062402 39,28,56,15,72,31,42,31,60,28,91,39,60,31,90,28,96,42,60,36,72,31,96,
%U A062402 42,63,60,98,39,90,60,91,56,90,31,168,72,91,63,124,42,144,63,84,60,144
%N A062402 a(n) = sigma(phi(n)).
%C A062402 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
%C A062402 Atanassov proves the above conjecture. - _Charles R Greathouse IV_, Dec 06 2016
%D A062402 Krassimir T. Atanassov, One property of φ and σ functions, Bull. Number Theory Related Topics 13 (1989), pp. 29-37.
%D A062402 A. Makowski and A. Schinzel, On the functions phi(n) and sigma(n), Colloq. Math. 13, 95-99 (1964).
%D A062402 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 13.
%H A062402 T. D. Noe, <a href="/A062402/b062402.txt">Table of n, a(n) for n = 1..10000</a>
%H A062402 G. L. Cohen, <a href="http://matwbn.icm.edu.pl/ksiazki/cm/cm74/cm7411.pdf">On a conjecture of Makowski and Schinzel</a>. Colloq. Math. 74, No. 1, 1-8 (1997).
%H A062402 A. Grytczuk, F. Luca and M. Wojtowicz, <a href="http://matwbn.icm.edu.pl/ksiazki/cm/cm86/cm8615.pdf">On a conjecture of Makowski and Schinzel concerning the composition of the arithmetic functions sigma and phi</a>, Colloq. Math. 86, No. 1, 31-36 (2000).
%H A062402 F. Luca and C. Pomerance, <a href="http://dx.doi.org/10.4064/cm92-1-10">On some problems of Makowski-Schinzel and Erdos concerning the arithmetical functions phi and sigma</a>, Colloq. Math. 92, No. 1, 111-130 (2002).
%F A062402 sigma(A062401(x)) = a(sigma(x)) or phi(a(x)) = A062401(phi(x)). - _Labos Elemer_, Jul 22 2004
%e A062402 a(9)= 12 because phi(9)= 6 and sigma(6)= 12.
%p A062402 with(numtheory); A062402:=n->sigma(phi(n)); seq(A062402(k), k=1..100); # _Wesley Ivan Hurt_, Nov 01 2013
%t A062402 Table[DivisorSigma[1, EulerPhi[n]], {n, 1, 80}] (* _Carl Najafi_, Aug 16 2011 *)
%o A062402 (PARI) a(n)=sigma(eulerphi(n));
%o A062402 vector(150,n,a(n))
%o A062402 (Haskell)
%o A062402 a062402 = a000203 . a000010  -- _Reinhard Zumkeller_, Jan 04 2013
%o A062402 (Python)
%o A062402 from sympy import divisor_sigma, totient
%o A062402 print([divisor_sigma(totient(n)) for n in range(1, 101)]) # _Indranil Ghosh_, Mar 18 2017
%o A062402 (Magma) [SumOfDivisors(EulerPhi(n)): n in [1..100]] //  _Marius A. Burtea_, Jan 19 2019
%Y A062402 Cf. A000203, A000010, A062401, A096852, A096857, A096994, A096995, A033632.
%K A062402 nonn
%O A062402 1,3
%A A062402 _Jason Earls_, Jul 08 2001

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