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Search: id:A109491
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| A109491 |
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Value of Product[DivisorSigma[1,k]/sd(k,2),k=1..n], where DivisorSigma[1,k] is the sum of divisors of k, and sd[k,b] is the sum of the digits of k represented in base b. |
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+0
2
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| 1, 3, 6, 42, 126, 756, 2016, 30240, 196560, 1769040, 7076160, 99066240, 462309120, 3698472960, 22190837760, 687915970560, 6191243735040, 120729252833280, 804861685555200, 16902095396659200, 180289017564364800
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OFFSET
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0,2
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COMMENT
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Surprisingly, the product in the definition is an integer for all values of n for which it has been calculated (1-300), whereas the corresponding base-3 product is not.
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EXAMPLE
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The divisors of 1-5 are {1}, {1,2}, {1,3}, {1,2,4}, and {1,5}, respectively, and the base-2 representations of 1-5 are 1,10,11,100,101, so a(5)=(1/1)(3/1)(4/2)(7/1)(6/2)=126.
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CROSSREFS
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Cf. A109489.
Sequence in context: A114038 A000222 A104271 this_sequence A085696 A079095 A002028
Adjacent sequences: A109488 A109489 A109490 this_sequence A109492 A109493 A109494
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Jun 29 2005
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