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A190144 Decimal expansion of Sum{k=2..infinity}(1/Prod{j=2..k} j’), where n’ is the arithmetic derivative of n. 5
2, 6, 0, 5, 0, 7, 2, 7, 0, 5, 2, 9, 7, 3, 2, 2, 8, 7, 0, 8, 0, 3, 4, 2, 6, 4, 1, 2, 4, 1, 8, 3, 8, 7, 8, 5, 1, 3, 7, 0, 8, 5, 7, 3, 6, 3, 2, 7, 6, 6, 3, 7, 2, 2, 4, 3, 8, 5, 8, 5, 0, 8, 4, 0, 7, 3, 1, 0, 5, 7, 5, 9, 3, 7, 1, 6, 1, 9, 7, 5, 1, 7, 0, 4, 7, 7, 4, 9, 9, 4, 5, 4, 7, 4, 8, 4, 5, 6, 1, 7, 0, 8, 8, 9, 4, 7, 7, 6, 2, 0, 9, 5, 9, 7, 8, 5, 2, 4, 4, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

The formally similar expansion of e, Sum{n=0..infinity} 1/n!, differ for 0.11320912… from the constant.

LINKS

Table of n, a(n) for n=2..121.

EXAMPLE

1/2’+1/(2’*3’)+1/(2’*3’*4’)+1/(2’*3’*4’*5’)+ 1/(2’*3’*4’*5’*6’)+... = 1+1+1/4+1/4+1/20+... = 2.605072705297...

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

  pfs:=ifactors(n)[2];

  f:=n*add(op(2, p)/op(1, p), p=pfs);

  b:=b*f; a:=a+1/b;

od;

print(evalf(a, 300));

end:

P(1000);

MATHEMATICA

digits = 120; d[0] = d[1] = 0; d[n_] := d[n] = n*Total[Apply[#2/#1&, FactorInteger[n], {1}]]; p[m_] := p[m] = Sum[1/Product[d[j], {j, 2, k}], {k, 2, m}] // RealDigits[#, 10, digits]& // First; p[digits]; p[m = 2*digits]; While[p[m] != p[m/2], m = 2*m]; p[m] (* Jean-François Alcover, Feb 21 2014 *)

CROSSREFS

Cf. A003415, A190145, A190146, A190147.

Sequence in context: A274402 A115252 A108431 * A019967 A241810 A156991

Adjacent sequences:  A190141 A190142 A190143 * A190145 A190146 A190147

KEYWORD

nonn,cons

AUTHOR

Paolo P. Lava, May 05 2011

STATUS

approved

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Last modified February 19 16:02 EST 2019. Contains 320311 sequences. (Running on oeis4.)