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A091627
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Number of ordered integer pairs (b,c) with 1 <= b,c <= n such that both roots of x^2+bx+c=0 are integers.
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9
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0, 0, 1, 2, 4, 5, 7, 8, 10, 12, 14, 15, 18, 19, 21, 23, 26, 27, 30, 31, 34, 36, 38, 39, 43, 45, 47, 49, 52, 53, 57, 58, 61, 63, 65, 67, 72, 73, 75, 77, 81, 82, 86, 87, 90, 93, 95, 96, 101, 103, 106, 108, 111, 112, 116, 118, 122, 124, 126, 127, 133, 134, 136, 139, 143
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OFFSET
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0,4
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COMMENTS
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Also number of ordered pairs of positive integers (i, j) such that i+j <= n and i*j <= n. - Seiichi Manyama, Sep 04 2021
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LINKS
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FORMULA
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G.f.: (1/(1 - x)) * (-x + Sum_{k>=1} x^(k^2)/(1 - x^k)). - Seiichi Manyama, Sep 04 2021
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MATHEMATICA
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PROG
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(PARI) a(n) = sum(i=1, n, sum(j=i, n-i, i*j<=n)); \\ Seiichi Manyama, Sep 04 2021
(PARI) N=66; x='x+O('x^N); concat([0, 0], Vec((-x+sum(k=1, sqrtint(N), x^k^2/(1-x^k)))/(1-x))) \\ Seiichi Manyama, Sep 04 2021
(Python)
from math import isqrt
m = isqrt(n)
return 0 if n == 0 else sum(n//k for k in range(1, m+1))-m*(m-1)//2-1 # Chai Wah Wu, Oct 07 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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