

A054980


Primitive eperfect numbers: primitive elements of the eperfect numbers (A054979).


9




OFFSET

1,1


COMMENTS

The nonprimitive eperfect numbers are obtained from the primitive ones by multiplying by m, if m is squarefree and relatively prime to the primitive eperfect 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, ePerfect 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



