login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers k such that k divides A306069(k).
2

%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