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Search: id:A062790
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| A062790 |
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Moebius transform of cototient function. |
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+0
1
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| 0, 1, 1, 1, 1, 2, 1, 2, 2, 4, 1, 3, 1, 6, 5, 4, 1, 6, 1, 5, 7, 10, 1, 6, 4, 12, 6, 7, 1, 8, 1, 8, 11, 16, 9, 8, 1, 18, 13, 10, 1, 12, 1, 11, 12, 22, 1, 12, 6, 20, 17, 13, 1, 18, 13, 14, 19, 28, 1, 13, 1, 30, 16, 16, 15, 20, 1, 17, 23, 24, 1, 16, 1, 36, 24, 19, 15, 24, 1, 20, 18, 40, 1, 19
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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Inverse Moebius transform of A051953 is A001065, the sum of proper divisors of n.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,2000
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FORMULA
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a(n)=Sum{f[n/d]*mu[d]}, where d divides n and f[x]=x-Phi[x]=A051953(x).
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EXAMPLE
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n=255,divisors={1,3,5,25,17,51,85,255}, A051953[255/d]={127,21,19,1,7,1,1,0},mu[d]={1,-1,-1,1,-1,1,1,-1}, the sum is a(255)=127-21-19+1-7+1+1+0=130-47=83.
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PROGRAM
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(PARI) { for (n=1, 2000, d=divisors(n); a=sum(k=1, length(d), (n/d[k] - eulerphi(n/d[k])) * moebius(d[k])); write("b062790.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 11 2009]
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CROSSREFS
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A051953, A001065.
Sequence in context: A151678 A151681 A131097 this_sequence A046640 A049823 A143775
Adjacent sequences: A062787 A062788 A062789 this_sequence A062791 A062792 A062793
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jul 19 2001
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EXTENSIONS
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OFFSET changed from 0,6 to 1,6 by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 11 2009
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