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A280076
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Numbers n such that Sum_{d|n} tau(d) = Product_{d|n} tau(d).
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11
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1, 4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 16129, 17161, 18769, 19321, 22201, 22801, 24649, 26569, 27889, 29929, 32041, 32761, 36481
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OFFSET
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1,2
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COMMENTS
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Union of 1 and A001248 (squares of primes).
Numbers n such that A007425(n) = Sum_{d|n} tau(d) = A211776(n) = Product_{d|n} tau(d) = 6.
Also squares of noncomposite numbers (A008578).
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LINKS
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FORMULA
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EXAMPLE
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9 is a term because Sum_{d|9} tau(d) = 1+2+3 = Product_{d|9} tau(d) = 1*2*3 = 6.
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MATHEMATICA
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Select[Range@ 37500, Total@ # == Times @@ # &@ Map[DivisorSigma[0, #] &, Divisors@ #] &] (* Michael De Vlieger, Dec 25 2016 *)
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PROG
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(Magma) [n: n in [1..1000000] | &*[NumberOfDivisors(d): d in Divisors(n)] eq &+[NumberOfDivisors(d): d in Divisors(n)]]
(PARI) isok(n) = my(d = divisors(n), nd = apply(numdiv, d)); vecsum(nd) == prod(k=1, #nd, nd[k]); \\ Michel Marcus, Jun 26 2017
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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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