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%I #5 May 28 2021 00:55:37
%S 1,275,277,3337,3353,3359,39675,39689,472467,797806459,9501109507
%N Numbers k such that k divides A306069(k).
%C The corresponding quotients A306069(k)/k are 1, 5, 5, 7, 7, 7, 9, 9, 11, 17, 19, ...
%C a(12) > 7.5*10^10, if it exists.
%e a(1) = 1 since A306069(1) = 1 is divisible by 1.
%e a(2) = 275 since A306069(275) = 1375 = 5 * 275 is divisible by 275.
%t f[p_, e_] := If[Mod[e, 2] == 1, (e + 1), e]; s[1] = 1; s[n_] := s[n] = s[n - 1] + Times @@ f @@@ FactorInteger[n]; Select[Range[40000], Divisible[s[#], #] &]
%Y Cf. A286324, A306069.
%Y The bi-unitary version of A050226.
%Y Similar sequences: A064610, A344732, A344733.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, May 27 2021