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A102408
Harmonic means associated with A090945.
2
1, 5, 6, 8, 9, 11, 10, 15, 15, 14, 17, 24, 24, 21, 13, 19, 27, 25, 29, 26, 44, 44, 29, 46, 39, 46, 27, 42, 47, 47, 54, 35, 41, 60, 51, 37, 48, 45, 49, 50, 49, 53, 77, 86, 86, 51, 96, 75, 70, 80, 99, 110, 81, 84, 102, 82, 96, 114, 53, 108, 115, 105, 116, 91
OFFSET
1,2
COMMENTS
A perfect number N = 2^(p-1)*M(p) (A000396), with associated Mersenne prime M(p) = 2^p -1 (A000668), has harmonic mean N*tau(N)/sigma(N) = p (A000043).
LINKS
FORMULA
a(n) = m*tau(m)/sigma(m), where m = A090945(n), tau = A000005 and sigma = A000203.
PROG
(PARI) lista(nn) = {for (n=1, nn, ab = sigma(n)/n; hm = numdiv(n)/ab; if ((type(hm) == "t_INT") && (ab != 2), print1(hm, ", ")); ); } \\ Michel Marcus, Oct 26 2013
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Lekraj Beedassy, Jan 07 2005
EXTENSIONS
a(1)=1 as well as a(29)=47 inserted and more terms added by Michel Marcus, Oct 26 2013
STATUS
approved