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Search: id:A121707
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| A121707 |
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Numbers n such that n^3 divides Sum[ k^n, {k,1,n-1} ] = A121706[n]. |
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2
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| 35, 55, 77, 95, 115, 119, 143, 155, 161, 187, 203, 209, 215, 221, 235, 247, 253, 275, 287, 295, 299, 323, 329, 335, 355, 371, 377, 391, 395, 403, 407, 413, 415, 437, 455, 473, 475, 493, 497, 515, 517, 527, 533, 535, 539, 551, 559, 575, 581, 583, 589, 611
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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All a(n) belong to A038509[n] Composite numbers with smallest prime factor >= 5. Many but not all a(n) belong to A060976[n] Odd nonprimes, c, which divide Bernoulli(2*c). Many a(n) are semiprimes. For example, semiprime a(n) that are multiples of 5 {7,11,19,23,31,43,47,59,67,71,79,83,103,107,127,131,139,151,163,167,179,191,199,...} = A002145[n] Primes of form 4n+3, except 3, or n>0; or Primes which are also Gaussian primes. Semiprime a(n) that are multiples of 7 {5,11,17,23,29,41,47,53,59,71,83,89,101,107,113,131,137,...} = A003627[n] Primes of form 3n-1, except 2, or n>1. Semiprime a(n) that are multiples of 11 {5,7,13,17,19,23,37,43,47,53,59,67,73,79,83,89,97,103,107,109,...} = Primes of form 4k+1 and 4k-1.
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MATHEMATICA
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Do[f=Sum[k^n, {k, 1, n-1}]; If[IntegerQ[f/n^3], Print[n]], {n, 1, 1200}]
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CROSSREFS
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Cf. A121706, A031971, A000312, A038509, A060976, A002145.
Sequence in context: A043135 A039312 A043915 this_sequence A157352 A090877 A048033
Adjacent sequences: A121704 A121705 A121706 this_sequence A121708 A121709 A121710
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 16 2006
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