A209873 Decimal expansion of Sum{k=2..infinity} (-1)^k/A165559(k).

0, 0, 3, 4, 7, 2, 8, 2, 5, 0, 4, 3, 3, 8, 6, 7, 0, 8, 1, 4, 7, 9, 1, 7, 6, 7, 3, 4, 2, 4, 6, 2, 3, 0, 5, 2, 7, 2, 7, 3, 7, 4, 5, 2, 4, 3, 1, 4, 7, 8, 0, 7, 4, 0, 5, 5, 1, 1, 2, 3, 8, 1, 4, 1, 5, 8, 4, 0, 3, 6, 9, 6, 8, 5, 5, 8, 2, 0, 2, 4, 3, 6, 2, 7, 7, 9

Offset: 0

Author

Paolo P. Lava, Apr 02 2012

Keywords

• nonn
• cons

Comments

Alternating sum of the reciprocals of the partial products of the arithmetic derivatives.

Examples

			0.003472825...
		

Links

• Ray Chandler, Table of n, a(n) for n = 0..85 (corrected by Ray Chandler, Jan 19 2019)

Crossrefs

Cf. A003415, A190144, A190145, A190146, A190147.

Programs

Maple

with(numtheory);
P:=proc(i)
local a, b, f, n, p, pfs;
a:=0; b:=1;
for n from 2 by 1 to i do
  f:= A003415(n);
  b:=b*f; a:=a+(-1)^n/b;
od;
print(evalf(a, 300));
end:
P(1000);

Mathematica

digits = 84; d[0] = d[1] = 0; d[n_] := d[n] = n*Total[Apply[#2/#1 &, FactorInteger[n], {1}]]; p[n_] := p[n] =  Sum[(-1)^k/Product[d[j], {j, 2, k}], {k, 2, n}] // RealDigits[#, 10, digits] & // First; p[digits]; p[n = 2*digits]; While[p[n] != p[n/2], n = 2*n]; Join[{0, 0}, p[n]] (* Jean-François Alcover, Feb 21 2014 *)