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%I #19 Jan 18 2024 02:42:15
%S 1,2,7,45,184,210,267,732,1282,3487,98374,137620,159597,645174,
%T 3949726,7867343,13215333,14153570,14262845,317186286,337222295,
%U 2788845412,10937683400,72836157215,95250594634
%N Numbers k such that A064603(k) is divisible by k.
%C Analogous sequences for various arithmetical functions are A050226, A056650, A064605-A064607, A064610, A064611, A048290, A062982, A045345.
%C a(22) > 2*10^9. - _Donovan Johnson_, Jun 21 2010
%C a(26) > 10^11, if it exists. - _Amiram Eldar_, Jan 18 2024
%F (Sum_{j=1..k} sigma_3(j)) mod k = A064603(k) mod k = 0.
%e Adding divisor-cube sums for j = 1..7 gives 1+9+28+73+126+252+344 = 833 = 7*119, which is divisible by 7, so 7 is a term and the integer quotient is 119.
%t A064603 = Accumulate[Table[DivisorSigma[3, k], {k, 1, 1000000}]]; Select[Range[Length[A064603]], Divisible[A064603[[#]], #] &] (* _Vaclav Kotesovec_, Jul 11 2021 *)
%Y Cf. A001158, A064603, A050226, A056650, A064605, A064607, A064610-A064612, A048290, A062982, A045345.
%K nonn,more
%O 1,2
%A _Labos Elemer_, Sep 24 2001
%E a(15)-a(21) from _Donovan Johnson_, Jun 21 2010
%E a(22)-a(25) from _Amiram Eldar_, Jan 18 2024
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