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 A307960 Decimal expansion of the asymptotic density of the coreful perfect numbers (A307958) that are generated from even primitives (A307959). 3
 9, 3, 6, 1, 0, 4, 7, 4, 5, 9, 0, 6, 8, 1, 6, 5, 6, 3, 8, 4, 5, 1, 6, 3, 0, 4, 5, 7, 8, 4, 4, 1, 1, 8, 5, 6, 1, 5, 5, 2, 8, 4, 2, 8, 7, 8, 2, 9, 8, 4, 3, 5, 3, 5, 6, 9, 4, 4, 2, 2, 0, 9, 1, 8, 9, 5, 8, 1, 1, 8, 4, 1, 5, 4, 6, 2, 4, 9, 0, 8, 6, 4, 7, 8, 1, 5, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET -2,1 COMMENTS Since the coreful perfect numbers are analogous to e-perfect numbers (A054979), the result of Hagis (see the formula and compare to A318645) can be also applied here. If there is no odd perfect number, then this constant is the asymptotic density of all the coreful perfect numbers. LINKS Amiram Eldar, Table of n, a(n) for n = -2..10000 Peter Hagis, Some results concerning exponential divisors, International Journal of Mathematics and Mathematical Sciences, Vol. 11, No. 2 (1988), pp. 343-349. FORMULA Equals Sum_{j>=1} beta(c(j))/c(j), where beta(k) = (6/Pi^2)*Product_{p|k}(p/(p+1)) and c(j) is the j-th even term of A307959. EXAMPLE 0.0093610474590681656384516304578441185615528428782... MATHEMATICA f[p_] := 1/(3 * (2^p-1) * 2^(2*p-1)); v = MersennePrimeExponent/@Range[25]; RealDigits[(6/Pi^2)*Total[f/@v], 10, 100][[1]] CROSSREFS Cf. A307958, A307959, A318645. Sequence in context: A153618 A171051 A230158 * A224235 A363716 A169849 Adjacent sequences: A307957 A307958 A307959 * A307961 A307962 A307963 KEYWORD nonn,cons AUTHOR Amiram Eldar, May 08 2019 STATUS approved

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Last modified August 7 03:39 EDT 2024. Contains 375008 sequences. (Running on oeis4.)