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Search: id:A056739
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| A056739 |
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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. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Contains A003598. In general n=p^iq^i => n|Sum[k=1..2p, k^n], where p, q=2p+1 prime (see Meyer ref).
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LINKS
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C. Meyer, On a conjecture arising from the OEIS
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MATHEMATICA
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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} ]
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CROSSREFS
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Cf. A001557.
Sequence in context: A021008 A059358 A084640 this_sequence A003598 A014858 A018368
Adjacent sequences: A056736 A056737 A056738 this_sequence A056740 A056741 A056742
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 25 2000
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