A189020 Sum_{k = 1..10^n} tau_4(k), where tau_4 is the number of ordered factorizations into 4 factors (A007426)

1, 89, 3575, 93237, 1951526, 35270969, 578262093, 8840109380, 128217432396, 1784942188189, 24045237260214, 315312623543840, 4042957241191810, 50862246063060180, 629513636928477232, 7681900592647818929

Offset

0,2

Comments

Using that tau_4 = tau_2 ** tau_2, where ** means Dirichlet convolution and tau_2 is (A000005), one can calculate a(n) faster than in O(10^n) operations - namely in O(10^(3n/4)) or even in O(10^(2n/3)). See links for details.

Links

Table of n, a(n) for n=0..15.

A. V. Lelechenko The summation of the multiplicative functions (in Russian)

Formula

a(n) = A061202(10^n) = sum(k = 1..10^n, A007426(n))

Crossrefs

Cf. A057494 - partial sums up to 10^n of the divisors function tau_2 (A000005), A180361 - of the unitary divisors function tau_2* (A034444), A180365 - of the 3-divisors function tau_3 (A007425).

Also see A072692 for such sums of the sum of divisors function (A000203), A084237 for sums of Moebius function (A008683), A064018 for sums of Euler totient function (A000010).

Sequence in context: A232321 A264161 A264068 * A322503 A157757 A017805

Adjacent sequences: A189017 A189018 A189019 * A189021 A189022 A189023

Keyword

nonn

Author

Andrew Lelechenko, Apr 15 2011

Status

approved