A175169 Numbers k that divide the sum of digits of 2^k.

1, 2, 5, 70

Offset: 1

Author

N. J. A. Sloane, Dec 03 2010

Keywords

• nonn
• base
• changed

Comments

No other terms <= 200000. - Harvey P. Dale, Dec 16 2010

No other terms <= 1320000. - Robert G. Wilson v, Dec 18 2010

There are almost certainly no further terms.

Crossrefs

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.

Programs

Mathematica

Select[Range[1000],Divisible[Total[IntegerDigits[2^#]],#]&] (* Harvey P. Dale, Dec 16 2010 *)

PARI

is(n)=sumdigits(2^n)%n==0 \\ Charles R Greathouse IV, Sep 06 2016