login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054980 Primitive e-perfect numbers: primitive elements of the e-perfect numbers (A054979). 9
36, 1800, 2700, 17424, 1306800, 4769856, 238492800, 357739200, 54531590400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The nonprimitive e-perfect numbers are obtained from the primitive ones by multiplying by m, if m is squarefree and relatively prime to the primitive e-perfect number.

a(10) > 10^15. - Donovan Johnson, Nov 22 2011

The following numbers also belong to this sequence; however, their actual positions are unknown: 168136940595306022660197936246988800, 11712310558743727210993873194516480000, 1307484087615221689700651798824550400000. - Andrew Lelechenko, Apr 01 2014

REFERENCES

R. K. Guy, Unsolved Problems In Number Theory, B17.

LINKS

Table of n, a(n) for n=1..9.

A. V. Lelechenko, Exponential and infinitary divisors, arXiv:1405.7597 (2014).

Jan Munch Pedersen, Exponential Perfect Numbers

Eric Weisstein's World of Mathematics, e-Perfect Number

EXAMPLE

180 = 36*5 (nonprimitive). 252 = 36*7 (nonprimitive). 1260 = 36*5*7 (nonprimitive). 1800 = 36*5^2 (primitive, 5^2 not squarefree and coprime to 36).

PROG

(PARI) eperfect(n)=my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2], d, f[i, 1]^d))==2*n

is(n)=if(!eperfect(n), 0, my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]==1&&eperfect(n/f[i, 1]), return(0))); 1) \\ Charles R Greathouse IV, Nov 22 2011

CROSSREFS

Cf. A051377, A054979, A160134 (complement).

Sequence in context: A190918 A219986 A113618 * A151640 A025754 A071128

Adjacent sequences:  A054977 A054978 A054979 * A054981 A054982 A054983

KEYWORD

nonn,more

AUTHOR

Jud McCranie, May 29 2000

EXTENSIONS

a(9) from Donovan Johnson, Nov 22 2011

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 20:57 EST 2019. Contains 319282 sequences. (Running on oeis4.)