

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
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OFFSET

2,1


COMMENTS

Since the coreful perfect numbers are analogous to eperfect 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



FORMULA

Equals Sum_{j>=1} beta(c(j))/c(j), where beta(k) = (6/Pi^2)*Product_{pk}(p/(p+1)) and c(j) is the jth even term of A307959.


EXAMPLE

0.0093610474590681656384516304578441185615528428782...


MATHEMATICA

f[p_] := 1/(3 * (2^p1) * 2^(2*p1)); v = MersennePrimeExponent/@Range[25]; RealDigits[(6/Pi^2)*Total[f/@v], 10, 100][[1]]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



