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A153816
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a(n) = Sum_{i=1..(10^n-1)/9} floor(((10^n-1)/9)/i).
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3
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1, 29, 542, 7967, 105225, 1308095, 15639310, 181976675, 2075608136, 23314508721, 258729364359, 2843136431305, 30989792180446, 335482200606705, 3610664794156597, 38665075822637767, 412235037037411453, 4378193158484415385, 46340359465948601163
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OFFSET
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1,2
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COMMENTS
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Generalized subsequences of A006218(n) are a(n) = A006218(T*A002275(n)), where T >= 1, a(n) = Sum_{i=1...n} floor(T*(10^n - 1)/9*i). For T=9 we have A095256, for T=1 this sequence. The motivation for such sequences is to count the elements of length n in a multiplication matrix m*m in base (T+1). In base 10 this gives T=9 and the number of elements of the multiplication matrix m*m of the length n=1,2,3,... digits is given by the sequence b(n) = a(n) - a(n-1), n >= 2, a(1)=23.
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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(PARI) a(n) = sum(i=1, (10^n-1)/9, ((10^n-1)/9)\i); \\ Michel Marcus, Jun 08 2018
(Python)
def a(n): t = (10**n-1)//9; return sum(t//i for i in range(1, t+1))
(Python)
from math import isqrt
def A153816(n): return -(s:=isqrt(m:=(10**n-1)//9))**2+(sum(m//k for k in range(1, s+1))<<1) # Chai Wah Wu, Oct 23 2023
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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