|
| |
|
|
A007357
|
|
Infinitary perfect numbers.
(Formerly M4267)
|
|
17
| |
|
|
6, 60, 90, 36720, 12646368, 22276800, 126463680, 4201148160, 28770487200, 287704872000, 1446875426304, 2548696550400, 14468754263040, 590325173932032, 3291641594841600, 8854877608980480, 32916415948416000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| 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.
|
|
|
REFERENCES
| G. L. Cohen, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| 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, Link to a section of The World of Mathematics.
|
|
|
FORMULA
| {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.
|
|
|
EXAMPLE
| 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.
|
|
|
CROSSREFS
| Cf. A129656 (infinitary abundant), A129657 (infinitary deficient)
Sequence in context: A185288 A189000 A007358 * A002827 A137498 A036283
Adjacent sequences: A007354 A007355 A007356 * A007358 A007359 A007360
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Eric Weisstein (eric(AT)weisstein.com), Jan 27, 2004.
|
| |
|
|
