The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A227882 Known number of n_multiperfect numbers that can produce an hemiperfect of abundancy (2*n-1)/2. 0
 1, 3, 19, 0, 87, 117, 0, 30, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS The hemiperfect that are obtained are coprime to p = 2*n-1. When p=2*n-1 is prime, if m is a n-multiperfect is such that valuation(m, p) = 1, then let's define k = m/p, sigma(k) = sigma(m/p) = sigma(m)/sigma(p) = (n*m)/(p+1) = (n*m)/(2*n) = m/2. So sigma(k)/k = m/(2*k) = (k*p)/(2*k) = p/2 = (2*n-1)/2. LINKS Achim Flammenkamp, The Multiply Perfect Numbers Page G. P. Michon, Multiperfect and hemiperfect numbers EXAMPLE a(2) = 1, since the only perfect number multiple of 3 is 6, and 6/3=2 has abundancy 3/2. a(3) = 3, since the 3 known hemiperfect of abundancy 5/2 are coprime to 5. a(5) = a(8) = a(11) = 0, since for those n, 2*n-1 is not prime. a(10) is also 0, since all known 10-multiperfect are at least divisible by 19^2. CROSSREFS Cf. A000396 (2), A005820 (3), A027687 (4), A046060 (5), A046061 (6), A007691 (integer abundancy). Cf. A141643 (5/2), A055153 (7/2), A141645 (9/2), A159271 (11/2), A160678 (13/2), A159907 (half-integer abundancy). Cf. A006254. Sequence in context: A001999 A157580 A101293 * A189799 A300946 A078096 Adjacent sequences:  A227879 A227880 A227881 * A227883 A227884 A227885 KEYWORD nonn,more AUTHOR Michel Marcus, Oct 25 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 19 02:40 EDT 2020. Contains 337175 sequences. (Running on oeis4.)