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A248517
Number of odd divisors > 1 in the numbers 1 through n, counted with multiplicity.
1
0, 0, 0, 1, 1, 2, 3, 4, 4, 6, 7, 8, 9, 10, 11, 14, 14, 15, 17, 18, 19, 22, 23, 24, 25, 27, 28, 31, 32, 33, 36, 37, 37, 40, 41, 44, 46, 47, 48, 51, 52, 53, 56, 57, 58, 63, 64, 65, 66, 68, 70, 73, 74, 75, 78, 81, 82, 85, 86, 87, 90, 91, 92, 97, 97, 100, 103, 104, 105, 108, 111
OFFSET
0,6
COMMENTS
Number of partitions of n into 3 parts such that the smallest part divides the "middle" part. - Wesley Ivan Hurt, Oct 21 2021
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = Sum_{j=1..n} A069283(j).
a(n) = A060831(n) - n.
a(n) = A006218(n) - A006218(floor(n/2)) - n. - Charles R Greathouse IV, Jun 18 2015
a(n) = Sum_{i=1..n-1} floor(floor(i/2)/(n-i)). - Wesley Ivan Hurt, Jan 30 2016
MAPLE
A248517 := proc(n)
add(A069283(j), j=1..n) ;
end proc:
MATHEMATICA
Table[Sum[Floor[Floor[i/2]/(n - i)], {i, n - 1}], {n, 0, 100}] (* Wesley Ivan Hurt, Jan 30 2016 *)
Join[{0}, Accumulate[Table[Count[Divisors[n], _?OddQ]-1, {n, 80}]]] (* Harvey P. Dale, Jan 06 2019 *)
Join[{0}, Accumulate[Table[DivisorSigma[0, n/2^IntegerExponent[n, 2]] - 1, {n, 1, 100}]]] (* Amiram Eldar, Jul 10 2022 *)
PROG
(PARI) a(n)=my(n2=n\2); sum(k=1, sqrtint(n), n\k)*2-sqrtint(n)^2-sum(k=1, sqrtint(n2), n2\k)*2+sqrtint(n2)^2-n \\ Charles R Greathouse IV, Jun 18 2015
(Python)
from math import isqrt
def A248517(n): return ((t:=isqrt(m:=n>>1))+(s:=isqrt(n)))*(t-s)+(sum(n//k for k in range(1, s+1))-sum(m//k for k in range(1, t+1))<<1)-n # Chai Wah Wu, Oct 23 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Jun 18 2015
STATUS
approved