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Numbers k such that k divides s(k), where s(1)=1, s(j) = s(j-1) + j*13^(j-1).
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%I #20 Jul 02 2021 01:57:32

%S 1,3,9,27,81,183,243,549,729,1647,2187,4941,6561,11163,14823,19683,

%T 33489,44469,59049,67161,100467,133407,177147,201483,301401,400221,

%U 531441,604449,680943,736941,870897,904203,1063611,1200663,1406721

%N Numbers k such that k divides s(k), where s(1)=1, s(j) = s(j-1) + j*13^(j-1).

%C From _Robert Israel_, Oct 07 2019: (Start)

%C Numbers k such that 144*k divides 1-(1-12*k)*13^k.

%C Contains all powers of 3 (A000244). (End)

%p filter:= proc(n) (1 - (1-12*n)*13 &^ n) mod (144*n) = 0 end proc:

%p select(filter, [$1..10^6]); # _Robert Israel_, Oct 07 2019

%t s[1]=1; s[n_]:=s[n]=s[n-1]+n*13^(n-1); Select[Range[1000], Divisible[s[#], #] &] (* _Amiram Eldar_, Nov 23 2018 *)

%Y Cf. A000244, A014928.

%K nonn

%O 1,2

%A _Olivier GĂ©rard_

%E More terms from _Sean A. Irvine_, Nov 23 2018