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).

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

Author

Amiram Eldar, May 10 2019

Keywords

• nonn
• more

Comments

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.

Examples

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

Crossrefs

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

Programs

Mathematica

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