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

2, 4, 22, 63, 4202, 4246, 444886, 1161238, 9362914, 26996486, 545614671, 1640386293, 2242930954, 2243031802, 2243065418, 2243115842, 18000691527

Offset: 1

Author

Joseph L. Pe, Jul 18 2002

Keywords

• nonn
• more

Comments

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

Examples

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

References

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

Crossrefs

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

Programs

Mathematica

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

Extensions

More terms from Robert G. Wilson v, Jul 27 2002

a(10)-a(17) from Giovanni Resta, Apr 03 2017