cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A348584 Numbers k such that k | A328258(k).

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%I A348584 #6 Oct 24 2021 09:37:53
%S A348584 1,12,56,180,992,16256,127400,441000,2646000,67100672,325458000,
%T A348584 2758909440,17179738112,274877382656
%N A348584 Numbers k such that k | A328258(k).
%C A348584 The corresponding ratios A113184(k)/k are 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -1, -1, ...
%C A348584 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 A348584 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 A348584 12 is a term since A328258(12) = -12 is divisible by 12.
%t A348584 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 A348584 The unitary version of A348583.
%Y A348584 A139256 is a subsequence.
%Y A348584 Cf. A000043, A034448, A327158, A328258.
%K A348584 nonn,more
%O A348584 1,2
%A A348584 _Amiram Eldar_, Oct 24 2021