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A057249

Numbers k such that k | 5^k + 4^k + 3^k + 2^k.

1, 2, 6, 7, 49, 78, 91, 133, 343, 539, 1014, 1309, 1578, 2401, 3367, 4459, 10231, 12103, 12246, 12691, 13182, 16807, 45619, 97193, 117649, 120883, 149989, 159198, 171366, 199283, 218491, 347263, 675703, 823543, 1100687, 1294139, 1327753, 1336699, 1486807

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..39.

MAPLE

A057249:=n->`if`(type((5^n+4^n+3^n+2^n)/n, integer), n, NULL); seq(A057249(n), n=1..10^6); # Wesley Ivan Hurt, Mar 09 2014

MATHEMATICA

Select[ Range[ 10^6 ], Mod[ PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ] + PowerMod[ 2, #, # ], # ] == 0 & ]

Select[Range[15*10^5], Mod[Total[PowerMod[Range[2, 5], #, #]], #]==0&] (* Harvey P. Dale, Mar 01 2023 *)

CROSSREFS

Sequence in context: A388428 A250547 A366061 * A246120 A300659 A155003