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 A057490 Numbers k that divide 8^k + 7^k + 6^k + 5^k + 4^k + 3^k + 2^k. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 LINKS Table of n, a(n) for n=1..52. 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 *) CROSSREFS Cf. A003595. Sequence in context: A037374 A056717 A072370 * A057253 A003595 A018697 Adjacent sequences: A057487 A057488 A057489 * A057491 A057492 A057493 KEYWORD nonn AUTHOR Robert G. Wilson v, Sep 22 2000 STATUS approved

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Last modified June 18 22:34 EDT 2024. Contains 373487 sequences. (Running on oeis4.)