A175552 Numbers k such that the digit sum of 167^k is divisible by k.

1, 2, 5, 7, 22, 490, 724, 778, 868, 994, 1109, 1390, 1415, 1462, 1642, 1739, 1829, 2146, 2362, 3136, 4954, 6437, 6628, 7103, 11200, 12424, 12863, 14242, 14249, 15059, 15203, 16222, 17140, 18353, 19192, 21233, 22853, 24106, 24574, 24833, 26896, 27652, 28253, 30323, 31306, 31594, 32386, 33790, 34985, 36184, 36310, 40673, 42196, 43931, 45911, 45983

Offset: 1

Author

N. J. A. Sloane, Dec 03 2010

Keywords

• base
• nonn

Comments

From Donovan Johnson, Dec 03 2010: (Start)

To generate the additional terms I used PFGW.exe to get the decimal expansion for each number of the form 167^n (n <= 50000). Then I wrote a program in powerbasic to read the pfgw.out file and get the digit sums.

The digit sum is 10 times the n value for terms a(5) to a(56). (End)

I believe that this sequence is finite. - N. J. A. Sloane, Dec 05 2010

Links

• Donovan Johnson, Table of n, a(n) for n = 1..129

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[10000], Mod[Total[IntegerDigits[167^#]], #] == 0 &]

Extensions

a(25)-a(56) from Donovan Johnson, Dec 03 2010