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 A054979 e-perfect numbers: numbers n such that the sum of the e-divisors (exponential divisors) of n equals 2n. 17
 36, 180, 252, 396, 468, 612, 684, 828, 1044, 1116, 1260, 1332, 1476, 1548, 1692, 1800, 1908, 1980, 2124, 2196, 2340, 2412, 2556, 2628, 2700, 2772, 2844, 2988, 3060, 3204, 3276, 3420, 3492, 3636, 3708, 3852, 3924, 4068, 4140, 4284, 4572, 4716 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The e-divisors (or exponential divisors) of x=Product p(i)^r(i) are all numbers of the form Product p(i)^s(i) where s(i) divides r(i) for all i. The number of e-divisors for n is A049419(n). - Jon Perry, Nov 13 2012 Conjecture: Every e-perfect number is divisible by 36, see A219016. - Jon Perry, Nov 13 2012 REFERENCES R. K. Guy, Unsolved Problems In Number Theory, B17. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, e-Perfect Number FORMULA {n: A051377(n) = 2*n} - R. J. Mathar, Oct 05 2017 EXAMPLE The e-divisors of 36 are 2*3, 4*3, 2*9 and 4*9 and the sum of these = 2*36, so 36 is e-perfect. MAPLE for n from 1 do     if A051377(n) = 2*n then         printf("%d, \n", n) ;     end if; end do: # R. J. Mathar, Oct 05 2017 MATHEMATICA ee[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; Select[Range[5000], ee[#] == 2 # &] (* T. D. Noe, Nov 14 2012 *) PROG (PARI) is(n)=my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2], d, f[i, 1]^d))==2*n \\ Charles R Greathouse IV, Nov 22 2011 CROSSREFS Cf. A051377, A054980, A219016. Sequence in context: A127657 A318100 A321145 * A102949 A211733 A211744 Adjacent sequences:  A054976 A054977 A054978 * A054980 A054981 A054982 KEYWORD nonn AUTHOR Jud McCranie, May 29 2000 STATUS approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)