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A371133
Decimal expansion of Sum_{n>=1} d(n)/n!, where d(n) is the number of divisors of n.
0
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
1,1
COMMENTS
This constant is irrational (Erdős and Straus, 1971).
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.
FORMULA
Equals Sum_{j,k>=1} 1/(j*k)! (Shamos, 2011, p. 4).
EXAMPLE
2.48106101979076269793744769639865739568689776121713...
MAPLE
with(numtheory); evalf(Sum(tau(n)/factorial(n), n = 1 .. infinity), 120)
MATHEMATICA
RealDigits[N[Sum[DivisorSigma[0, n]/n!, {n, 1, 500}], 120]][[1]]
PROG
(PARI) suminf(k=1, numdiv(k)/k!)
CROSSREFS
Sum_{n>=1} sigma_k(n)/n!: this sequence (k=0), A227988 (k=1), A227989 (k=2), A307036 (k=3), A359060 (k=4).
Sequence in context: A124221 A339415 A097625 * A010743 A072032 A365814
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 12 2024
STATUS
approved