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 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 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

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