A056739 Numbers n such that n | 10^n + 9^n + 8^n + 7^n + 6^n + 5^n + 4^n + 3^n + 2^n + 1^n.

1, 5, 11, 25, 55, 121, 125, 275, 365, 605, 625, 925, 1331, 1375, 2365, 3025, 3125, 6655, 6875, 14641, 15125, 15625, 22625, 27565, 32125, 33275, 34375, 73205, 75625, 78125, 123365, 161051, 166375, 171875, 366025, 378125, 390625, 541717, 660605

Offset

1,2

Comments

Contains A003598. In general n=p^iq^i => n|Sum[k=1..2p, k^n], where p, q=2p+1 prime (see Meyer ref).

Links

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

C. Meyer, On a conjecture arising from the OEIS

Mathematica

Do[ If[ Mod[ PowerMod[ 10, n, n ] + 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[700000], Divisible[Total[Range[10]^#], #]&] (* Harvey P. Dale, Nov 24 2014 *)
Select[Range[700000], Mod[Total[PowerMod[Range[10], #, #]], #]==0&] (* Harvey P. Dale, Feb 23 2023 *)

Crossrefs

Cf. A001557.

Sequence in context: A167238 A084640 A337481 * A003598 A014858 A355243

Adjacent sequences: A056736 A056737 A056738 * A056740 A056741 A056742

Keyword

nonn

Author

Robert G. Wilson v, Aug 25 2000

Status

approved