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A275196
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Odd numbers n such that sigma(n) does not divide sigma(n^3).
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1
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9, 25, 27, 49, 63, 75, 81, 99, 117, 121, 125, 135, 147, 153, 169, 171, 175, 207, 225, 243, 245, 261, 275, 289, 297, 325, 333, 343, 361, 363, 369, 375, 387, 405, 425, 441, 475, 477, 507, 513, 525, 529, 531, 539, 549, 567, 575, 603, 605, 625, 637, 639, 675, 693, 711, 725, 729
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OFFSET
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1,1
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COMMENTS
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All terms are composite since sigma(p) = p + 1 and sigma(p^3) = p^3 + p^2 + p + 1 = (p + 1)(p^2 + 1) for p prime.
An odd number n with prime factorization Product_i p_i^(e_i) is in this sequence if and only if Product_i ((p_i^(3*e_i + 1) - 1)/(p_i^(e_i + 1) - 1)) is not an integer.
Nonsquare terms of this sequence are 27, 63, 75, 99, 117, 125, 135, 147, 153, 171, 175, 207, 243, 245, 261, 275, ...
Terms that are not perfect powers are 63, 75, 99, 117, 135, 147, 153, 171, 175, 207, 245, 261, 275, 297, 325, 333, 363, 369, 375, ...
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LINKS
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EXAMPLE
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63 is a term because sigma(63^3) = 437200 is not divisible by sigma(63) = 104.
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MATHEMATICA
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Select[2Range[400] - 1, Not[Divisible[DivisorSigma[1, #^3], DivisorSigma[1, #]]] &] (* Alonso del Arte, Jul 20 2016 *)
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PROG
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(PARI) isok(n) = sigma(n^3) % sigma(n) != 0 && n % 2 == 1
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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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