Vol. 57, No. 2, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Some new results on odd perfect numbers

G. G. Dandapat, John L. Hunsucker and Carl Pomerance

Vol. 57 (1975), No. 2, 359–364
Abstract

If m is a multiply perfect number (σ(m) = tm for some integer t), we ask if there is a prime p with m = pan, (pa,n) = 1(n) = pa, and σ(pa) = tn. We prove that the only multiply perfect numbers with this property are the even perfect numbers and 672. Hence we settle a problem raised by Suryanarayana who asked if odd perfect numbers necessarily had such a prime factor. The methods of the proof allow us also to say something about odd solutions to the equation σ(σ(n)) = 2n.

Mathematical Subject Classification
Primary: 10A40
Milestones
Received: 16 October 1974
Published: 1 April 1975
Authors
G. G. Dandapat
John L. Hunsucker
Carl Pomerance
Mathematics Department
Dartmouth College
Kemeny Hall
Dartmouth College
Hanover NH 03755
United States
www.math.dartmouth.edu/~carlp