A057255 Numbers k such that k | 7^k + 6^k + 5^k + 4^k + 3^k.

1, 5, 25, 95, 125, 305, 425, 625, 1525, 3125, 7625, 15625, 18605, 24625, 38125, 78125, 93025, 129625, 133475, 190625, 201605, 265625, 390625, 465125, 492575, 537715, 953125, 957695, 1134905, 1484375, 1639375, 1886425, 1953125, 2325625, 3621875, 4223335, 4765625, 5674525, 7940675, 8392075, 8837375, 9765625

Offset

1,2

Links

Table of n, a(n) for n=1..42.

Mathematica

Select[ Range[ 10^6 ], Mod[ PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ], # ] == 0 & ]
With[{c=Mod[Total[Table[PowerMod[k, #1, #1], {k, 3, 7}]], #1]==0&}, Select[Range[10^6], c]] (* Harvey P. Dale, Mar 07 2026 *)

Prog

(Python)
def ok(k): return k and sum(pow(m, k, k) for m in range(3, 8))%k == 0
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Mar 08 2026

Crossrefs

Sequence in context: A265929 A297452 A147177 * A134140 A225011 A228457

Adjacent sequences: A057252 A057253 A057254 * A057256 A057257 A057258

Keyword

nonn

Author

Robert G. Wilson v, Sep 21 2000

Extensions

a(29) onward from Michael S. Branicky, Mar 08 2026

Status

approved