A057490 Numbers k that divide 8^k + 7^k + 6^k + 5^k + 4^k + 3^k + 2^k.

1, 5, 7, 25, 35, 49, 125, 175, 245, 301, 343, 455, 625, 875, 1225, 1295, 1435, 1505, 1715, 1765, 2107, 2191, 2401, 3125, 4375, 6125, 7525, 8575, 10535, 11375, 12005, 12943, 14063, 14749, 15625, 16807, 21875, 22295, 30625, 35875, 37625, 42875, 52675, 60025, 64715, 70315, 73745, 78125, 80375, 84035, 90601, 93275

Offset: 1

Author

Robert G. Wilson v, Sep 22 2000

Keywords

• nonn

Comments

Contains A003595. The first term not in A003595 is 301. Is 1 the only term not divisible by 5 or 7? - Robert Israel, Feb 22 2017

No term is divisible by 3. 5 and 7 are the only primes in this sequence. - Altug Alkan, Feb 23 2017

Crossrefs

Cf. A003595.

Programs

Maple

select(t -> add(i &^ t, i=2..8) mod t = 0, [$1..10^6]); # Robert Israel, Feb 22 2017

Mathematica

Select[ Range[ 10^5 ], Mod[ PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ] + PowerMod[ 2, #, # ], # ] == 0 & ]
Select[Range[100000],Mod[Total[PowerMod[Range[2,8],#,#]],#]==0&] (* Harvey P. Dale, Jul 28 2021 *)