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Numbers k such that k*sigma_0(k) is divisible by (k - sigma_0(k)).
6

%I #35 Oct 04 2024 00:22:22

%S 3,4,6,8,12,18,24,36,40,60,84,156,180,600

%N Numbers k such that k*sigma_0(k) is divisible by (k - sigma_0(k)).

%C No other term < 10000000. - _Michel Marcus_, Jun 02 2013

%C No other term multiple of 12 below 10^9. - _M. F. Hasler_, Apr 16 2022

%F A352483(a(n)) = 1. - _Bernard Schott_, Mar 23 2022

%t nsiQ[n_]:=Module[{s=DivisorSigma[0,n]},IntegerQ[(n*s)/(n-s)]]; Select[ Range[3,600],nsiQ] (* _Harvey P. Dale_, Dec 05 2019 *)

%o (PARI) isok(n) = {my(nd = numdiv(n)); type(n*nd/(n-nd)) == "t_INT"} \\ _Michel Marcus_, Jun 02 2013

%o (PARI) is_A146566(n,d=numdiv(n))={n*d%(n-d)==0} \\ _M. F. Hasler_, Apr 16 2022

%Y Cf. A000005, A049820, A352483.

%K nonn,more

%O 1,1

%A _Ctibor O. Zizka_, Nov 01 2008

%E Corrected and extended by _Michel Marcus_, Jun 02 2013