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%I #6 Oct 24 2021 09:37:53
%S 1,12,56,180,992,16256,127400,441000,2646000,67100672,325458000,
%T 2758909440,17179738112,274877382656
%N Numbers k such that k | A328258(k).
%C The corresponding ratios A113184(k)/k are 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -1, -1, ...
%C If p is a Mersenne exponent (A000043), then 2^p*(2^p-1) (twice an even perfect number) is a term with ratio A328258(k)/k = -1.
%C If there exists an odd term k, then it is a unitary multiply-perfect number (A327158), since A328258(k) = A034448(k) for an odd k.
%e 12 is a term since A328258(12) = -12 is divisible by 12.
%t f[p_, e_] := 1 - (-1)^p*(p^e); s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[3*10^6], Divisible[s[#], #] &]
%Y The unitary version of A348583.
%Y A139256 is a subsequence.
%Y Cf. A000043, A034448, A327158, A328258.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Oct 24 2021