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%I #21 Sep 08 2022 08:45:06
%S 1,10,12,24,615,4066,7960,30432,49260,133686,440286,1201644,6640812,
%T 126953125,411106256,1046704882,11046706752,44588839041
%N Numbers n such that sum k/d(k) is an integer, where d(k) is the k-th divisor of n (the divisors of n are in decreasing order).
%C a(12) > 11*10^5. - _Emeric Deutsch_, Mar 05 2005
%C 8*10^11 < a(19) <= 2343594361433 = 13^10*17. It seems that the numbers 5^(13*k-3)*13 and 13^(17*k-7)*17, for k > 0, are terms. - _Giovanni Resta_, Dec 06 2019
%e The divisors of 615 are [615,205,123,41,15,5,3,1] and 1/615+2/205+3/123+4/41+5/15+6/5+7/3+8/1 = 12 is an integer hence 615 is in the sequence.
%t Select[Range[441000],IntegerQ[Total[Range[DivisorSigma[0,#]]/ Reverse[ Divisors[ #]]]]&] (* _Harvey P. Dale_, May 23 2019 *)
%o (Magma) [k:k in [1..500000]|IsIntegral(&+[m/Reverse(Divisors(k))[m]:m in [1..#Divisors(k)]])]; // _Marius A. Burtea_, Dec 06 2019
%Y Cf. A056538, A073082.
%K nonn,more
%O 1,2
%A _Benoit Cloitre_, Aug 17 2002
%E More terms from _Emeric Deutsch_, Mar 05 2005
%E a(12)-a(17) from Lambert Klasen (lambert.klasen(AT)gmx.net), Jul 15 2005
%E a(18) from _Giovanni Resta_, Dec 06 2019
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