A371133 Decimal expansion of Sum_{n>=1} d(n)/n!, where d(n) is the number of divisors of n.
2, 4, 8, 1, 0, 6, 1, 0, 1, 9, 7, 9, 0, 7, 6, 2, 6, 9, 7, 9, 3, 7, 4, 4, 7, 6, 9, 6, 3, 9, 8, 6, 5, 7, 3, 9, 5, 6, 8, 6, 8, 9, 7, 7, 6, 1, 2, 1, 7, 1, 3, 1, 6, 2, 0, 7, 2, 3, 6, 9, 3, 3, 7, 1, 7, 5, 5, 2, 0, 4, 4, 1, 0, 9, 0, 9, 3, 0, 3, 3, 3, 6, 9, 2, 6, 7, 2, 0, 2, 4, 8, 3, 2, 4, 7, 1, 2, 9, 3, 8, 4, 8, 6, 4, 4
Offset: 1
Examples
2.48106101979076269793744769639865739568689776121713...
Links
- Paul Erdős and Ernst G. Straus, Some number theoretic results, Pacific Journal of Mathematics, Vol. 36, No. 3 (1971), pp. 635-646.
- Michael Ian Shamos, Overcounting Functions, 2011.
Crossrefs
Programs
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Maple
with(numtheory); evalf(Sum(tau(n)/factorial(n), n = 1 .. infinity), 120)
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Mathematica
RealDigits[N[Sum[DivisorSigma[0, n]/n!, {n, 1, 500}], 120]][[1]] -
PARI
suminf(k=1,numdiv(k)/k!)
Formula
Equals Sum_{j,k>=1} 1/(j*k)! (Shamos, 2011, p. 4).
Comments