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A069288
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Number of odd divisors of n <= sqrt(n).
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39
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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 3, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 3, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 3, 1, 1, 3, 1, 2, 2, 1, 1, 2, 3, 1, 2, 1, 1, 3, 1, 2, 2, 1, 2, 3, 1, 1, 3, 2, 1, 2, 1, 1, 4
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OFFSET
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1,9
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COMMENTS
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LINKS
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FORMULA
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G.f.: Sum_{n>=1} 1/(1-q^(2*n-1)) * q^((2*n-1)^2). [Joerg Arndt, Mar 04 2010]
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EXAMPLE
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The inferior odd divisors for selected n are the columns below:
n: 1 9 30 90 225 315 630 945 1575 2835 4410 3465 8190 6930
--------------------------------------------------------------------
1 3 5 9 15 15 21 27 35 45 63 55 65 77
1 3 5 9 9 15 21 25 35 49 45 63 63
1 3 5 7 9 15 21 27 45 35 45 55
1 3 5 7 9 15 21 35 33 39 45
1 3 5 7 9 15 21 21 35 35
1 3 5 7 9 15 15 21 33
1 3 5 7 9 11 15 21
1 3 5 7 9 13 15
1 3 5 7 9 11
1 3 5 7 9
1 3 5 7
1 3 5
1 3
1
(End)
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MATHEMATICA
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odn[n_]:=Count[Divisors[n], _?(OddQ[#]&&#<=Sqrt[n ]&)]; Array[odn, 100] (* Harvey P. Dale, Nov 04 2017 *)
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PROG
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(PARI) a(n) = my(ir = sqrtint(n)); sumdiv(n, d, (d % 2) * (d <= ir)); \\ Michel Marcus, Jan 14 2014
(Haskell)
a069288 n = length $ takeWhile (<= a000196 n) $ a182469_row n
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CROSSREFS
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Positions of first appearances are A334853.
A055396 selects the least prime index.
A061395 selects the greatest prime index.
- Odd -
A026424 lists numbers with odd Omega.
A027193 counts odd-length partitions.
- Inferior divisors -
A033676 selects the greatest inferior divisor.
A033677 selects the least superior divisor.
A060775 selects the greatest strictly inferior divisor.
A063538 lists numbers with a superior prime divisor.
A063539 lists numbers without a superior prime divisor.
A063962 counts inferior prime divisors.
A064052 lists numbers with a properly superior prime divisor.
A140271 selects the least properly superior divisor.
A217581 selects the greatest inferior divisor.
A333806 counts strictly inferior prime divisors.
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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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