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A056754 Numbers n such that n | 9^n + 8^n + 7^n + 6^n + 5^n + 4^n + 3^n + 2^n + 1^n. 0
1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 243, 375, 405, 423, 625, 675, 729, 765, 801, 895, 1017, 1125, 1175, 1215, 1875, 2025, 2125, 2187, 3125, 3375, 3645, 4755, 5625, 6075, 6561, 9375, 9585, 10125, 10935, 15625, 16875, 17925, 18225, 19683 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..47.

MATHEMATICA

Do[ If[ Mod[ PowerMod[ 9, n, n ] + PowerMod[ 8, n, n ] + PowerMod[ 7, n, n ] + PowerMod[ 6, n, n ] + PowerMod[ 5, n, n ] + PowerMod[ 4, n, n ] + PowerMod[ 3, n, n ] + PowerMod[ 2, n, n ] + 1, n ] == 0, Print[ n ] ], {n, 1, 10^6} ]

Select[Range[20000], Divisible[Total[Range[2, 9]^# ]+1, #]&] (* Harvey P. Dale, Oct 09 2019 *)

CROSSREFS

Cf. A001556.

Sequence in context: A056741 A057235 A057289 * A003593 A120027 A018586

Adjacent sequences:  A056751 A056752 A056753 * A056755 A056756 A056757

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Aug 25 2000

STATUS

approved

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Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)