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0, 0, 0, 1, 1, -1, -1, 0, 2, 2, 2, 1, 1, 1, -1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 4, 4, 6, 5, 5, 1, 1, 4, 4, 4, 2, 5, 5, 5, 5, 4, 4, 0, 0, 1, -1, -1, -1, 0, 6, 10, 10, 11, 11, 11, 11, 10, 10, 10, 10, 5, 5, 5, 5, 12, 12, 8, 8, 9, 9, 7, 7, 8, 8, 8, 10, 11, 9, 7, 7, 8
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,9
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COMMENTS
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a(n) = one-half of (number of pairs (i,j) in [1..n] X [1..n] with integral geometric mean sqrt(i*j)) - (number of pairs (i,j) in [1..n] X [1..n] with integral harmonic mean 2*i*j/(i+j)).
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LINKS
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FORMULA
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 0, add(
`if`(irem(2*i*n, i+n)=0, -1, 0)+
`if`(issqr(i*n), 1, 0), i=1..n-1)+a(n-1))
end:
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PROG
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(Python)
from sympy.ntheory.primetest import is_square
def A362933(n): return sum((1 if T else -1) for x in range(1, n+1) for y in range(1, x) if (T:=is_square(x*y))^(not (x*y<<1)%(x+y))) # Chai Wah Wu, Aug 29 2023
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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