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Numbers k such that Sum_{d|k} tau(d)/d is an integer, where tau(x) = A000005(x).
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%I #35 Feb 24 2024 01:02:37

%S 1,2,9,18,105,210,24375,48750,133848,18780741,18780965,37561482,

%T 37561930,121486365,169028685,242972730,338057370,360988056,676114740,

%U 1120584213,1285201500,1352229480,2241168426,2776831200,5352575025,5408917920,7437262140,10705150050

%N Numbers k such that Sum_{d|k} tau(d)/d is an integer, where tau(x) = A000005(x).

%C Also k such that k divides A007429(k).

%C Also k such that k divides A211780(k). - _Jaroslav Krizek_, Sep 28 2014

%C a(28) > 10^10. - _Giovanni Resta_, Jun 10 2013

%C a(33) > 5*10^10. - _Hiroaki Yamanouchi_, Oct 05 2014

%H Hiroaki Yamanouchi, <a href="/A068978/b068978.txt">Table of n, a(n) for n = 1..32</a>

%H Hiroaki Yamanouchi, <a href="/A068978/a068978.txt">Conjectured table of n, a(n) for n = 1..200</a>

%t t = {}; n = 0; While[n++ <= 20000000, If[Mod[Total[DivisorSigma[1, Divisors[n]]], n] == 0, AppendTo[t, n]]]; t (* _Jayanta Basu_, Apr 03 2013 *)

%o (PARI) for(n=1, 20000000, if(denominator( sumdiv(n,d, numdiv(d)/d)) ==1, print1(n,",")))

%K nonn

%O 1,2

%A _Benoit Cloitre_, Apr 06 2002

%E More terms from _Rick L. Shepherd_, Jun 23 2002

%E a(12)-a(27) from _Giovanni Resta_, Jun 10 2013

%E a(28) from _Hiroaki Yamanouchi_, Oct 05 2014