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A341594
Number of strictly superior odd divisors of n.
29
0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 2, 0, 1, 2, 1, 1, 3, 1, 1, 0, 1, 1, 2, 1, 1, 2, 2, 0, 2, 1, 1, 1, 1, 1, 3, 0, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 2, 1, 0, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 0, 1, 1, 3, 1, 1, 2, 1, 1, 4
OFFSET
1,15
COMMENTS
We define a divisor d|n to be strictly superior if d > n/d. Strictly superior divisors are counted by A056924 and listed by A341673.
LINKS
EXAMPLE
The a(n) divisors for n = 3, 15, 45, 105, 315, 405, 945, 1575, 1890:
3 5 9 15 21 27 35 45 45
15 15 21 35 45 45 63 63
45 35 45 81 63 75 105
105 63 135 105 105 135
105 405 135 175 189
315 189 225 315
315 315 945
945 525
1575
MATHEMATICA
Table[Length[Select[Divisors[n], OddQ[#]&&#>n/#&]], {n, 100}]
PROG
(PARI) A341594(n) = sumdiv(n, d, (d%2)*(d>(n/d))); \\ Antti Karttunen, Feb 23 2021
CROSSREFS
On odd indices, equals A056924 (number of strictly superior divisors).
The inferior version is A069288.
Positions of zeros are A116882.
Positions of nonzero terms are A116883.
The strictly inferior version is A333805.
The version for squarefree instead of odd divisors is A341595.
The version for prime instead of odd divisors is A341642.
The version for prime-power instead of odd divisors is A341644.
The superior version is A341675.
A033676 selects the greatest inferior divisor.
A033677 selects the smallest superior divisor.
A038548 counts superior (or inferior) divisors.
A140271 selects the smallest strictly superior divisor.
A207375 lists central divisors.
A341673 lists strictly superior divisors.
- Strictly Inferior: A060775, A070039, A333806, A341596, A341674.
- Strictly Superior: A048098, A064052, A238535, A341643, A341645, A341646.
Sequence in context: A351567 A284203 A375106 * A368774 A005087 A050332
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 23 2021
STATUS
approved