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%I #13 May 15 2019 04:52:06
%S 1,2,3,4,35,44,111,123,1105,1900,2920,12452,17889,34200,65067,716148,
%T 14134055,179040201,221709100,221743300,221766100,221788900,
%U 1120968741,1272582040,1441454511,7339101375
%N Numbers k such that usigma(k) = round(zeta(2)/zeta(3)*k), where usigma(k) is the sum of unitary divisors of k (A034448).
%C The unitary version of A072355.
%C zeta(2)/zeta(3) is the asymptotic mean of the unitary abundancy index usigma(k)/k (A306633).
%C a(27) > 10^10.
%e 35 is in the sequence since usigma(35) = 48, and (zeta(2)/zeta(3)) * 35 = 47.895... has a round value of 48.
%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); meanAb = Zeta[2]/Zeta[3]; Select[Range[10^6], usigma[#] == Round[meanAb*#] &]
%Y Cf. A002117, A013661, A034448, A072355, A074920, A306633.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, May 10 2019