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%I #29 Aug 16 2021 21:33:13
%S 1,2,5,70
%N Numbers k that divide the sum of digits of 2^k.
%C No other terms <= 200000. - _Harvey P. Dale_, Dec 16 2010
%C No other terms <= 1320000. - _Robert G. Wilson v_, Dec 18 2010
%C There are almost certainly no further terms.
%t Select[Range[200000],Divisible[Total[IntegerDigits[2^#]],#]&]
%t (* Harvey P. Dale, Dec 16 2010 *)
%o (PARI) is(n)=sumdigits(2^n)%n==0 \\ _Charles R Greathouse IV_, Sep 06 2016
%Y Sum of digits of k^n mod n: (k=2) A000079, A001370, A175434, A175169; (k=3) A000244, A004166, A175435, A067862; (k=5) A000351, A066001, A175456; (k=6) A000400, A066002, A175457, A067864; (k=7) A000420, A066003, A175512, A067863; (k=8) A062933; (k=13) A001022, A175527, A175528, A175525; (k=21) A175589; (k=167) A175558, A175559, A175560, A175552.
%K nonn,base
%O 1,2
%A _N. J. A. Sloane_, Dec 03 2010