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

1,2

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

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

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

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

Sequence in context: A355641 A363701 A353193 * A240564 A189719 A158698

Adjacent sequences: A102405 A102406 A102407 * A102409 A102410 A102411

Keyword

nonn

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