A010805 17th powers: a(n) = n^17.
0, 1, 131072, 129140163, 17179869184, 762939453125, 16926659444736, 232630513987207, 2251799813685248, 16677181699666569, 100000000000000000, 505447028499293771, 2218611106740436992, 8650415919381337933, 30491346729331195904, 98526125335693359375, 295147905179352825856, 827240261886336764177
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).
Crossrefs
Programs
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Magma
[n^17: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011
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Maple
A010805 := n -> n^17; # M. F. Hasler, Jul 03 2025
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Mathematica
Range[0,15]^17 (* Harvey P. Dale, Sep 14 2011 *)
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PARI
for(n=0,15,print1(n^17,", ")) \\ Derek Orr, Feb 27 2017
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PARI
apply( {A010805(n)=n^17}, [0..20]) \\ Defines the function and (as "proof of concept") applies it to [0..20]. - M. F. Hasler, Jul 03 2025 -
Python
A010805 = lambda n: n**17 # M. F. Hasler, Jul 03 2025
Formula
Totally multiplicative sequence with a(p) = p^17 for prime p. Multiplicative sequence with a(p^e) = p^(17e). - Jaroslav Krizek, Nov 01 2009
From Ilya Gutkovskiy, Feb 27 2017: (Start)
Dirichlet g.f.: zeta(s-17).
Sum_{n>=1} 1/a(n) = zeta(17) = A013675. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 65535*zeta(17)/65536. - Amiram Eldar, Oct 09 2020