A102408 Harmonic means associated with A090945.

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

Author

Lekraj Beedassy, Jan 07 2005

Keywords

• nonn

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

• Amiram Eldar, Table of n, a(n) for n = 1..930

Crossrefs

Cf. A000005, A000043, A000203, A000396, A000668, A090945.

Programs

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

Formula

a(n) = m*tau(m)/sigma(m), where m = A090945(n), tau = A000005 and sigma = A000203.

Extensions

a(1)=1 as well as a(29)=47 inserted and more terms added by Michel Marcus, Oct 26 2013