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A190145 Decimal expansion of Sum{k=1..infinity}(1/Prod{j=1..k} j^j’), where n’ is the arithmetic derivative of n. 5
1, 6, 6, 7, 4, 4, 7, 9, 3, 5, 8, 0, 3, 6, 9, 3, 9, 0, 5, 5, 8, 0, 5, 6, 7, 5, 1, 2, 8, 7, 3, 3, 9, 6, 0, 2, 0, 3, 9, 4, 4, 7, 8, 0, 1, 1, 3, 8, 1, 7, 7, 1, 6, 7, 0, 0, 5, 3, 7, 2, 8, 2, 2, 7, 6, 2, 0, 5, 8, 9, 3, 2, 9, 0, 2, 5, 2, 7, 7, 9, 1, 7, 0, 2, 4, 5, 2, 5, 4, 9, 9, 7, 7, 0, 8, 8, 1, 2, 2, 4, 8, 2, 4, 1, 6, 2, 6, 3, 3, 6, 8, 6, 1, 5, 1, 1, 1, 8, 9, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

1

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+1/2+1/6+1/1536+... = 1.6674479358036...

MAPLE

with(numtheory);

P:=proc(i)

local a, b, c, d, f, n, p, pfs, s;

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*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/Product[j^d[j], {j, 2, 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, A190146, A190147

Sequence in context: A196737 A070058 A160057 * A195103 A152485 A256684

Adjacent sequences:  A190142 A190143 A190144 * A190146 A190147 A190148

KEYWORD

nonn,cons

AUTHOR

Paolo P. Lava, May 05 2011

STATUS

approved

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Last modified April 6 15:23 EDT 2020. Contains 333276 sequences. (Running on oeis4.)