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%I #4 Jul 07 2022 02:07:19
%S 1,2,3,11,13,50,81,96,395,640,59136,65719,632621,1342813,2137073,
%T 2755370,3446370,10860093,321939569,1872591111,8858043355
%N Numbers k such that A272718(k) is divisible by k.
%C Numbers k such that the mean value of A018804 over the range 1..k is an integer.
%C The corresponding quotients are 1, 2, 3, 13, 16, 80, 141, 172, 865, 1500, 219530, 246058, 2804048, 6259092, 10263121, 13445321, 17051542, 57521176, 2036840289, 12849666590, 64967828053, ... .
%C a(22) > 6.5*10^10, if it exists.
%e 11 is a term since A061201(11) = 143 = 11 * 13 is divisible by 11.
%t f[p_,e_] := (e*(p-1)/p+1)*p^e; pillai[1] = 1; pillai[n_] := Times @@ f @@@ FactorInteger[n]; seq = {}; sum = 0; Do[sum += pillai[n]; If[Divisible[sum, n], AppendTo[seq, n]], {n, 1, 10^6}]; seq
%Y Cf. A018804, A272718.
%Y Similar sequences: A045345, A050226, A056550, A064605, A064606, A064607, A064610, A064611, A064612, A048290.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Jul 06 2022
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