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A062402
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a(n) = sigma(phi(n)).
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75
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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;
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OFFSET
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1,3
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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FORMULA
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EXAMPLE
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a(9)= 12 because phi(9)= 6 and sigma(6)= 12.
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MAPLE
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MATHEMATICA
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Table[DivisorSigma[1, EulerPhi[n]], {n, 1, 80}] (* Carl Najafi, Aug 16 2011 *)
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PROG
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(PARI) a(n)=sigma(eulerphi(n));
vector(150, n, a(n))
(Haskell)
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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