文档介绍：HANDBOOK
OF NUMBER THEORY II
by
J. Sandor´
Babes¸-Bolyai University of Cluj
Department of Mathematics puter Science
Cluj-Napoca, Romania
and
B. Crstici
formerly the Technical University of Timis¸oara
Timis¸oara Romania
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON
A . Catalogue record for this book is available from the Library of Congress.
ISBN 1-4020-2546-7 (HB)
ISBN 1-4020-2547-5 (e-book)
Published by Kluwer Academic Publishers,
. Box 17, 3300 AA Dordrecht, herlands.
Sold and distributed in North, Central and South America
by Kluwer Academic Publishers,
101 Philip Drive, Norwell, MA 02061, .
In all other countries, sold and distributed
by Kluwer Academic Publishers,
. Box 322, 3300 AH Dordrecht, herlands.
Printed on acid-free paper
All Rights Reserved
C 2004 Kluwer Academic Publishers
No part of this work may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming, recording
or otherwise, without written permission from the Publisher, with the exception
of any material supplied specifically for the purpose of being entered
and executed on puter system, for exclusive use by the purchaser of the work.
Printed in herlands.
Contents
PREFACE 7
BASIC SYMBOLS 9
BASIC NOTATIONS 10
1 PERFECT NUMBERS: OLD AND NEW ISSUES;
PERSPECTIVES 15
Introduction .............................. 15
Some historical facts ......................... 16
Even perfect numbers ......................... 20
Odd perfect numbers ......................... 23
Perfect, multiperfect and multiply perfect numbers ......... 32
Quasiperfect, almost perfect, and pseudoperfect
numbers ................................ 36
Superperfect and related numbers .................. 38
Pseudoperfect, weird and harmonic numbers ............. 42
Unitary, bi-unitary, infinitary-perfect and related n