A074920 -id:A074920 - cp's OEIS frontend

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

Joseph L. Pe, Jul 18 2002

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

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

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

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

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

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

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

A308045 Numbers k such that usigma(k) = round(zeta(2)/zeta(3)*k), where usigma(k) is the sum of unitary divisors of k (A034448).

Original entry on oeis.org

1, 2, 3, 4, 35, 44, 111, 123, 1105, 1900, 2920, 12452, 17889, 34200, 65067, 716148, 14134055, 179040201, 221709100, 221743300, 221766100, 221788900, 1120968741, 1272582040, 1441454511, 7339101375

Offset: 1

Amiram Eldar, May 10 2019

The unitary version of A072355.
zeta(2)/zeta(3) is the asymptotic mean of the unitary abundancy index usigma(k)/k (A306633).
a(27) > 10^10.

			35 is in the sequence since usigma(35) = 48, and (zeta(2)/zeta(3)) * 35 = 47.895... has a round value of 48.

Cf. A002117, A013661, A034448, A072355, A074920, A306633.

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); meanAb = Zeta[2]/Zeta[3]; Select[Range[10^6], usigma[#] == Round[meanAb*#] &]

cp's OEIS Frontend

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

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