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Search: id:A006087
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| A006087 |
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Unitary harmonic means H(n) of the unitary harmonic numbers (A006086).
(Formerly M0452)
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+0
2
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| 1, 2, 3, 4, 4, 7, 7, 6, 9, 13, 10, 13, 10, 7, 11, 15, 10, 15, 9, 12, 7, 17, 12, 18, 16, 14, 19, 20, 19, 12, 15, 20, 10, 20, 18, 22, 19, 13, 12, 13, 17, 29, 18, 33, 20, 23, 29, 34, 23, 22, 31, 38, 24, 23, 38, 33, 37, 40, 19, 38, 24, 37, 29, 40, 22, 34, 24, 33
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Let d(n) and sigma(n) be number and sum of unitary divisors of n; then unitary harmonic mean of unitary divisors is H(n)=n*d(n)/sigma(n).
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REFERENCES
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P. Hagis, Jr., and G. Lord, Unitary harmonic numbers, Proc. Amer. Math. Soc., 51 (1975), 1-7.
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MAPLE
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A034444 := proc(n) 2^nops(ifactors(n)[2]) ; end: A034448 := proc(n) local ans, i, ifs ; ans :=1 ; ifs := ifactors(n)[2] ; for i from 1 to nops(ifs) do ans := ans*(1+ifs[i][1]^ifs[i][2]) ; od ; RETURN(ans) ; end: A006086 := proc(n) n*A034444(n)/A034448(n) ; end: for n from 1 to 5000000 do uhn := A006086(n) : if type(uhn, 'integer') then printf("%d, ", uhn) ; fi ; od : - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 06 2007
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PROGRAM
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(PARI) {ud(n)=2^omega(n)} {sud(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))} {H(n)=n*ud(n)/sud(n)} for(n=1, 10000000, if(((n*ud(n))%sud(n))==0, print1(H(n)", "))) - Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
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CROSSREFS
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Cf. A006086.
Sequence in context: A053273 A049988 A079247 this_sequence A136330 A028298 A047966
Adjacent sequences: A006084 A006085 A006086 this_sequence A006088 A006089 A006090
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KEYWORD
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nonn,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 06 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
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