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A072355 Numbers k such that sigma(k) = (Pi^2)*(k/6) rounded off (where 0.5 is rounded to 0). 3

%I #14 May 10 2019 17:55:02

%S 2,4,22,63,4202,4246,444886,1161238,9362914,26996486,545614671,

%T 1640386293,2242930954,2243031802,2243065418,2243115842,18000691527

%N Numbers k such that sigma(k) = (Pi^2)*(k/6) rounded off (where 0.5 is rounded to 0).

%C In 1838 Dirichlet showed that the average value of sigma(n) is (Pi^2)*(n/6) for large n (see Tattersall).

%D Tattersall, J. "Elementary Number Theory in Nine Chapters", Cambridge University Press, 1999.

%e sigma(444886) = 731808 = (Pi^2 * 444886)/6 rounded off; so 444886 is a term of the sequence.

%t Select[Range[10^6], Round[(Pi^2 * #)/6] == DivisorSigma[1, # ] &]

%Y Cf. A013661 (Pi^2/6), A074920.

%K nonn,more

%O 1,1

%A _Joseph L. Pe_, Jul 18 2002

%E More terms from _Robert G. Wilson v_, Jul 27 2002

%E a(10)-a(17) from _Giovanni Resta_, Apr 03 2017

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)