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A277169
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Product of squares of proper divisors of n.
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1
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1, 1, 1, 4, 1, 36, 1, 64, 9, 100, 1, 20736, 1, 196, 225, 4096, 1, 104976, 1, 160000, 441, 484, 1, 191102976, 25, 676, 729, 614656, 1, 729000000, 1, 1048576, 1089, 1156, 1225, 78364164096, 1, 1444, 1521, 4096000000, 1, 5489031744, 1, 3748096, 4100625, 2116, 1, 28179280429056, 49, 6250000
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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(n) = n^(sigma_0(n)-2).
a(n) = 1 if n is prime or n = 1 (A008578).
a(n) = n if n is square of prime (A001248).
a(n) = n^2 if n is multiplicatively perfect number (A007422).
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EXAMPLE
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a(6) = 36 because 6 has 3 proper divisors {1,2,3} and 1^2*2^2*3^2 = 36.
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MAPLE
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seq(n^(numtheory:-tau(n)-2), n=1..50); # Robert Israel, Nov 13 2016
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MATHEMATICA
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Table[n^(DivisorSigma[0, n] - 2), {n, 1, 50}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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