|
%I #17 Jun 04 2021 03:15:37
%S 1,35,37,1015,27417,27421,27449,27453,19774739,530743781,530743799,
%T 530743807,530743813
%N Places k where A064608(k) (partial sums of unitary tau) is divisible by k.
%C The corresponding quotients are 1, 3, 3, 5, 7, 7, 7, 7, 11, 13, 13, 13, 13, ...
%C a(14) > 7.5*10^10, if it exists. - _Amiram Eldar_, Jun 04 2021
%F {n: A064608(n) == 0 (mod n)}.
%e For n = 37, the sum A064608(37) = 1+2+2+2+2+4+2+...+4+4+4+2 = 111 = 3*37, so 37 is in the sequence.
%t s[1] = 1; s[n_] := s[n] = s[n - 1] + 2^PrimeNu[n]; Select[Range[30000], Divisible[s[#], #] &] (* _Amiram Eldar_, Jun 04 2021 *)
%Y Cf. A064608.
%Y Analogous "integer-mean" sequences for various arithmetical functions are A050226, A056650, A064605, A064606, A064607, A048290, A063986, A063971, A064911, A062982, A045345.
%K nonn,more
%O 1,2
%A _Labos Elemer_, Sep 24 2001
%E a(10)-a(13) from _Donovan Johnson_, Jul 20 2012
|
