

A327576


Decimal expansion of the constant that appears in the asymptotic formula for average order of the number of infinitary divisors function (A037445).


2



3, 6, 6, 6, 2, 5, 2, 7, 6, 9, 4, 5, 3, 8, 1, 9, 0, 9, 5, 5, 6, 5, 3, 2, 7, 2, 0, 6, 8, 7, 0, 0, 1, 5, 6, 3, 0, 3, 3, 6, 1, 2, 1, 5, 5, 9, 7, 1, 0, 0, 9, 2, 7, 3, 0, 3, 7, 5, 8, 7, 5, 1, 5, 3, 0, 5, 7, 4, 7, 5, 3, 3, 4, 4, 7, 4, 9, 2, 5, 0, 7, 5, 7, 9, 0, 5, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


REFERENCES

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7.5, pp. 5354.


LINKS

Table of n, a(n) for n=0..86.
Graeme L. Cohen and Peter Hagis, Jr., Arithmetic functions associated with infinitary divisors of an integer, International Journal of Mathematics and Mathematical Sciences, Vol. 16, No. 2 (1993), pp. 373383.


FORMULA

Equals Limit_{n>oo} A327573(n)/(2 * n^3 * log(n)).
Equals (1/2) * Product_{P} (1  1/(P+1)^2), where P are numbers of the form p^(2^k) where p is prime and k >= 0 (A050376).


EXAMPLE

0.366625276945381909556532720687001563033612155971009...


MATHEMATICA

m = 1000; em = 10; f[x_] := Sum[Log[1  1/(1 + 1/x^(2^e))^2], {e, 0, em}]; c = Rest[CoefficientList[Series[f[x], {x, 0, m}], x]*Range[0, m]]; $MaxExtraPrecision = 1500; RealDigits[(1/2)*Exp[f[1/2] + f[1/3]]* Exp[NSum[Indexed[c, k]*(PrimeZetaP[k]  (1/2)^k  (1/3)^k)/k, {k, 2, m}, NSumTerms > m, WorkingPrecision > m]], 10, 100][[1]]


CROSSREFS

Cf. A037445, A050376, A327573.
Cf. A059956 (corresponding constant for unitary divisors), A306071 (biunitary).
Sequence in context: A187601 A113737 A292165 * A040006 A155067 A094011
Adjacent sequences: A327573 A327574 A327575 * A327577 A327578 A327579


KEYWORD

nonn,cons


AUTHOR

Amiram Eldar, Sep 17 2019


STATUS

approved



