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

1,1

Comments

This constant is irrational (Erdős and Straus, 1971).

Links

Table of n, a(n) for n=1..105.

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

Cf. A000005, A336334.

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

Adjacent sequences: A371130 A371131 A371132 * A371134 A371135 A371136

Keyword

nonn,cons

Author

Amiram Eldar, Mar 12 2024

Status

approved