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Search: id:A091045
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| 1, 18, 307, 5220, 88741, 1508598, 25646167, 435984840, 7411742281, 125999618778, 2141993519227, 36413889826860, 619036127056621, 10523614159962558, 178901440719363487, 3041324492229179280, 51702516367896047761
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OFFSET
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1,2
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COMMENT
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17^a(n) is highest power of 17 dividing (17^n)!.
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FORMULA
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a(n)= sum(17^k, k=0..n-1) = (17^n-1)/16.
G.f.: x/((1-17*x)*(1-x))= (1/(1-17*x) - 1/(1-x))/16.
For analogues with primes 2, 3, 5, 7, 11, 13, ... see: A000225, A003462, A003463, A023000, A016123, A091030, ...
a(n)=17*a(n-1)+1 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009]
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EXAMPLE
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For n=2, a(2)=17*1+1=18; n=3, a(3)=17*18+1=307; n=4, a(4)=17*307+1=5220 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009]
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PROGRAM
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(Other) sage: [gaussian_binomial(n, 1, 17) for n in xrange(1, 18)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
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CROSSREFS
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Sequence in context: A161599 A083451 A097831 this_sequence A158532 A049660 A001027
Adjacent sequences: A091042 A091043 A091044 this_sequence A091046 A091047 A091048
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KEYWORD
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nonn,easy,new
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jan 23 2004
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