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

1,2

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.

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]]

Crossrefs

Cf. A375538 (numerators).

Sequence in context: A360213 A055321 A092300 * A048916 A366313 A260797

Adjacent sequences: A375536 A375537 A375538 * A375540 A375541 A375542

Keyword

nonn,frac

Author

Amiram Eldar, Aug 19 2024

Status

approved