A375539 Denominator of the asymptotic mean over the positive integers of the maximum exponent in the prime factorization of the largest prime(n)-smooth divisor function.

1, 10, 36540, 636617813832, 369693143251781030056182487680, 418823586043433867400108534336212749520449347490879717721482735332151276111078704000

Offset: 1

Author

Amiram Eldar, Aug 19 2024

Keywords

• nonn
• frac

Comments

The numbers of digits of the terms are 1, 2, 5, 12, 30, 84, 215, 537, 1237, 2929, 6775, 15483, 35184, ... .

Links

• Amiram Eldar, Table of n, a(n) for n = 1..8
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Cf. A375538 (numerators).

Programs

Mathematica

d[k_, n_] := Product[1 - 1/Prime[i]^k, {i, 1, n}]; f[n_] := Sum[k * (d[k+1, n] - d[k, n]), {k, 1, Infinity}]; Denominator[Array[f, 6]]