A057289 Numbers n such that n | 12^n + 11^n + 10^n + 9^n + 8^n + 7^n + 6^n + 5^n + 4^n + 3^n.

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 243, 345, 375, 405, 625, 675, 729, 1025, 1125, 1215, 1863, 1875, 2025, 2187, 2375, 2875, 3125, 3375, 3645, 4395, 5625, 5875, 6075, 6561, 8145, 9225, 9375, 10125, 10935, 14015, 14523, 15525, 15625

Offset

1,2

Links

Table of n, a(n) for n=1..46.

Mathematica

Select[ Range[ 10^5 ], Mod[ PowerMod[ 12, #, # ] + PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ], # ] == 0 & ]
Select[Range[16000], Divisible[Total[Range[3, 12]^#], #]&] (* Harvey P. Dale, Dec 06 2013 *)
Select[Range[16000], Mod[Total[PowerMod[Range[3, 12], #, #]], #]==0&] (* Harvey P. Dale, Feb 12 2022 *)

Crossrefs

Sequence in context: A231114 A056741 A057235 * A056754 A003593 A120027

Adjacent sequences: A057286 A057287 A057288 * A057290 A057291 A057292

Keyword

nonn

Author

Robert G. Wilson v, Sep 22 2000

Status

approved