This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007357 Infinitary perfect numbers.
(Formerly M4267)
6, 60, 90, 36720, 12646368, 22276800, 126463680, 4201148160, 28770487200, 287704872000, 1446875426304, 2548696550400, 14468754263040, 590325173932032, 3291641594841600, 8854877608980480, 32916415948416000 (list; graph; refs; listen; history; text; internal format)



Numbers N whose sum of infinitary divisors equals 2*N: A049417(N)=2*N. - Joerg Arndt, Mar 20 2011

6 is the only infinitary perfect number which is also perfect number (A000396). 6 is also the only squarefree infinitary perfect number. - Vladimir Shevelev, Mar 02 2011


G. L. Cohen, personal communication.

A. V. Lelechenko, The Quest for the Generalized Perfect Numbers, in Theoretical and Applied Aspects of Cybernetics, TAAC 2014, Kiev; http://taac.org.ua/files/a2014/proceedings/UA-2-Andrew%20Lelechenko-440.pdf

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..17.

G. L. Cohen, On an integer's infinitary divisors, Math. Comp., 54 (1990), 395-411.

Jan Munch Pedersen, Known infinitary perfect numbers.

Eric Weisstein's World of Mathematics, Infinitary Perfect Number.


{n: A049417(n) = 2*n}. - R. J. Mathar, Mar 18 2011

a(n)==0 (mod 6). Thus there are no odd infinitary perfect numbers. - Vladimir Shevelev, Mar 02 2011


Let n=90. Its unique expansion over distinct terms of A050376 is 90=2*5*9. Thus the infinitary divisors of 90 are 1,2,5,9,10,18,45,90. The number of such divisors is 2^3, i.e., the cardinality of the set of all subsets of the set {2,5,9}. The sum of such divisors is (2+1)*(5+1)*(9+1)=180 and the sum of proper such divisors is 90=n. Thus 90 is in the sequence. - Vladimir Shevelev, Mar 02 2011


Cf. A129656 (infinitary abundant), A129657 (infinitary deficient).

Sequence in context: A185288 A189000 A007358 * A002827 A137498 A250070

Adjacent sequences:  A007354 A007355 A007356 * A007358 A007359 A007360




N. J. A. Sloane.


More terms from Eric W. Weisstein, Jan 27 2004



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

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 03:42 EST 2016. Contains 278993 sequences.