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A046659
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Numbers whose sum of divisors and sum of cubes of divisors are relatively prime.
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1
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1, 4, 9, 25, 36, 100, 121, 225, 289, 484, 529, 841, 900, 1089, 1156, 1681, 2116, 2209, 2601, 2809, 3364, 3481, 4356, 4761, 5041, 6724, 6889, 7225, 7569, 7921, 8836, 10201, 10404, 11236, 11449, 12769, 13225, 13924, 15129, 17161, 18769, 19044
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OFFSET
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1,2
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COMMENTS
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It appears that (a) all the numbers are squares, (b) the number of divisors is a power of 3.
It can be shown that this is a subset of A028982.
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LINKS
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EXAMPLE
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k=100 has 9 divisors whose sum is 217 = 7*31 and whose sum of cubes is 1149823 = 19*73*829; gcd(217, 1149823) = 1, so 100 is in the sequence.
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MATHEMATICA
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Select[Range[20000], GCD[DivisorSigma[1, #], DivisorSigma[3, #]]==1&] (* Harvey P. Dale, Feb 19 2011 *)
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PROG
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(PARI) isok(n) = gcd(sigma(n), sigma(n, 3)) == 1; \\ Michel Marcus, May 14 2018
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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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