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A190147 Decimal expansion of Sum{k=1..infinity}(1/Sum{j=1..k} j^j’), where n’ is the arithmetic derivative of n. 5
1, 5, 0, 7, 8, 1, 0, 6, 6, 7, 6, 2, 2, 8, 9, 8, 2, 8, 3, 8, 3, 3, 1, 5, 3, 9, 0, 3, 7, 6, 5, 3, 7, 7, 7, 2, 7, 2, 4, 7, 3, 4, 6, 8, 8, 5, 1, 9, 3, 8, 9, 5, 5, 8, 5, 5, 3, 1, 9, 1, 3, 9, 0, 8, 6, 3, 0, 1, 2, 5, 3, 8, 1, 3, 3, 9, 5, 8, 9, 8, 9, 1, 1, 6, 7, 1, 4, 7, 5, 0, 5, 2, 5, 1, 0, 6, 3, 0, 6, 1, 3, 1, 7, 1, 2, 7, 1, 9, 4, 9, 9, 2, 2, 7, 3, 6, 6, 2, 4, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..120.

EXAMPLE

1/1^1’+1/(1^1’+2^2’)+1/(1^1’+2^2’+3^3’)+1/(1^1’+2^2’+3^3’+4^4’)+... = 1+1/3+1/6+1/262+... = 1.50781066762289...

MAPLE

with(numtheory);

P:=proc(i)

local a, b, f, n, p, pfs;

a:=0; b:=0;

for n from 1 by 1 to i do

  pfs:=ifactors(n)[2];

  f:=n*add(op(2, p)/op(1, p), p=pfs);

  b:=b+n^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/Sum[j^d[j], {j, 1, k}], {k, 1, 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, A190144, A190145, A190146.

Sequence in context: A180660 A221711 A200400 * A108745 A114124 A155827

Adjacent sequences:  A190144 A190145 A190146 * A190148 A190149 A190150

KEYWORD

nonn,cons

AUTHOR

Paolo P. Lava, May 05 2011

STATUS

approved

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Last modified February 27 08:51 EST 2020. Contains 332301 sequences. (Running on oeis4.)