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A302976
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a(n) = tau(n)^n mod n^tau(n).
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2
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0, 0, 8, 17, 7, 208, 30, 0, 0, 8576, 112, 0, 80, 22864, 36199, 159681, 155, 0, 116, 40062976, 83791, 142928, 255, 26138902528, 68, 302656, 362152, 454885376, 60, 544999124224, 374, 0, 226279, 629152, 399674, 27234498115233, 76, 956704, 956539, 3361080344576
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OFFSET
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1,3
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COMMENTS
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tau(n) = the number of the divisors of n (A000005).
tau(n)^n > n^tau(n) for all n > 3.
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LINKS
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FORMULA
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EXAMPLE
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For n = 8; a(8) = 0 because tau(8)^8 mod 8^tau(8) = 4^8 mod 8^4 = 65536 mod 4096 = 0.
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MATHEMATICA
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PowerMod[#[[2]], #[[1]], #[[1]]^#[[2]]]&/@Table[{n, DivisorSigma[0, n]}, {n, 40}] (* Harvey P. Dale, Jan 08 2023 *)
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PROG
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(Magma) [(NumberOfDivisors(n)^n) mod (n^NumberOfDivisors(n)): n in[1..100]]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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