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A206032
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a(n) = Product_{d|n} sigma(d) where sigma = A000203.
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15
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1, 3, 4, 21, 6, 144, 8, 315, 52, 324, 12, 28224, 14, 576, 576, 9765, 18, 73008, 20, 95256, 1024, 1296, 24, 25401600, 186, 1764, 2080, 225792, 30, 26873856, 32, 615195, 2304, 2916, 2304, 1302170688, 38, 3600, 3136, 128595600, 42, 84934656, 44, 762048, 584064
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OFFSET
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1,2
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COMMENTS
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Sequence is not the same as A206031(n): a(66) = 429981696, A206031(66) = 35831808.
In sequence a(n) are multiplied all values of sigma(d) of all divisors d of numbers n, in sequence A206031 are multiplied only distinct values of sigma(d) of all divisors d of numbers n.
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LINKS
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FORMULA
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a(p) = p+1, a(pq) = ((p+1)*(q+1))^2 for p, q = distinct primes.
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EXAMPLE
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For n=6 -> divisors d of 6: 1,2,3,6; corresponding values k of sigma(d): 1,3,4,12; a(6) = Product of k = 1*3*4*12 = 144. For n=66 -> divisors d of 66: 1,2,3,6,11,22,33,66; corresponding values k of sigma(d): 1,3,4,12,12,36,48,144; a(66) = Product of k = 1*3*4*12*12*36*48*144 = 429981696.
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MATHEMATICA
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Table[Times @@ DivisorSigma[1, Divisors[n]], {n, 100}] (* T. D. Noe, Feb 10 2012 *)
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PROG
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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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