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A303277
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If n = Product (p_j^k_j) then a(n) = (Sum (k_j))^(Sum (p_j)).
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4
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1, 1, 1, 4, 1, 32, 1, 9, 8, 128, 1, 243, 1, 512, 256, 16, 1, 243, 1, 2187, 1024, 8192, 1, 1024, 32, 32768, 27, 19683, 1, 59049, 1, 25, 16384, 524288, 4096, 1024, 1, 2097152, 65536, 16384, 1, 531441, 1, 1594323, 6561, 33554432, 1, 3125, 128, 2187, 1048576, 14348907, 1, 1024, 65536
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OFFSET
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1,4
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LINKS
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FORMULA
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a(p^k) = k^p where p is a prime.
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EXAMPLE
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a(48) = a(2^4 * 3^1) = (4 + 1)^(2 + 3) = 5^5 = 3125.
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MATHEMATICA
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Join[{1}, Table[PrimeOmega[n]^DivisorSum[n, # &, PrimeQ[#] &], {n, 2, 55}]]
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PROG
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(PARI) a(n) = my(f=factor(n)); vecsum(f[, 2])^vecsum(f[, 1]); \\ Michel Marcus, Apr 21 2018
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CROSSREFS
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Cf. A000142, A000312, A001222, A002110, A007504, A008472, A008474, A008477, A022559, A034387, A039697, A088865, A263653, A285769.
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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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