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 A062402 a(n) = sigma(phi(n)). 65
 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 (list; graph; refs; listen; history; text; internal format)
 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 T. D. Noe, Table of n, a(n) for n = 1..10000 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 CROSSREFS Cf. A000203, A000010, A062401, A096852, A096857, A096994, A096995, A033632. Sequence in context: A122978 A119347 A323774 * A294015 A156838 A274845 Adjacent sequences:  A062399 A062400 A062401 * A062403 A062404 A062405 KEYWORD nonn AUTHOR Jason Earls, Jul 08 2001 STATUS approved

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Last modified July 9 18:08 EDT 2020. Contains 335545 sequences. (Running on oeis4.)