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A189020 Sum_{k = 1..10^n} tau_4(k), where tau_4 is the number of ordered factorizations into 4 factors (A007426) 0
1, 89, 3575, 93237, 1951526, 35270969, 578262093, 8840109380, 128217432396, 1784942188189, 24045237260214, 315312623543840, 4042957241191810, 50862246063060180, 629513636928477232, 7681900592647818929 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Andrew Lelechenko, Apr 15 2011
STATUS
approved

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Last modified April 15 05:10 EDT 2024. Contains 371667 sequences. (Running on oeis4.)