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Search: id:A097764
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| A097764 |
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Numbers of the form (kp)^p for prime p and k=1,2,3,.... |
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+0
3
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| 4, 16, 27, 36, 64, 100, 144, 196, 216, 256, 324, 400, 484, 576, 676, 729, 784, 900, 1024, 1156, 1296, 1444, 1600, 1728, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3125, 3136, 3364, 3375, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5476, 5776, 5832, 6084, 6400
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The polynomial x^n - n is reducible over the integers for n in this sequence.
A result of Vahlen shows that the polynomial x^n - n is reducible over the integers for n in this sequence and no other n.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
A. Schinzel, Problems and results on polynomials
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MATHEMATICA
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nMax=10000; lst={}; n=1; While[p=Prime[n]; p^p<=nMax, k=1; While[(k*p)^p<=nMax, AppendTo[lst, (k*p)^p]; k++ ]; n++ ]; Union[lst]
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CROSSREFS
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Cf. A084746 (least k such that n^k-k is prime).
Cf. A097792 (numbers of the form 4k^4 or (kp)^p).
Sequence in context: A050707 A046346 A134330 this_sequence A072873 A072653 A008478
Adjacent sequences: A097761 A097762 A097763 this_sequence A097765 A097766 A097767
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KEYWORD
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easy,nice,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Aug 24 2004
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