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A069288 Number of odd divisors of n <= sqrt(n). 39
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
COMMENTS
a(n) = #{d : d = A182469(n,k), d <= A000196(n), k=1..A001227(n)}. - Reinhard Zumkeller, Apr 05 2015
LINKS
FORMULA
G.f.: Sum_{n>=1} 1/(1-q^(2*n-1)) * q^((2*n-1)^2). [Joerg Arndt, Mar 04 2010]
EXAMPLE
From Gus Wiseman, Feb 11 2021: (Start)
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)
MATHEMATICA
odn[n_]:=Count[Divisors[n], _?(OddQ[#]&&#<=Sqrt[n ]&)]; Array[odn, 100] (* Harvey P. Dale, Nov 04 2017 *)
PROG
(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
-- Reinhard Zumkeller, Apr 05 2015
CROSSREFS
Positions of first appearances are A334853.
A055396 selects the least prime index.
A061395 selects the greatest prime index.
- Odd -
A000009 counts partitions into odd parts (A066208).
A026424 lists numbers with odd Omega.
A027193 counts odd-length partitions.
A067659 counts strict partitions of odd length (A030059).
- Inferior divisors -
A033676 selects the greatest inferior divisor.
A033677 selects the least superior divisor.
A038548 counts inferior divisors.
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.
Sequence in context: A115574 A115577 A115570 * A152831 A097795 A161076
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 14 2002
STATUS
approved

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Last modified March 19 03:21 EDT 2024. Contains 370952 sequences. (Running on oeis4.)