STATUS
proposed
approved
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Revision History for A069288
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
editing
proposed
FORMULA
G.f.: sum(Sum_{n>=1, } 1/(1-q^(2*n-1)) * q^((2*n-1)^2) ) . [Joerg Arndt, Mar 04 2010]
FORMULA
G.f.: sum(n>=1, 1/(1-q^(2*n-1)) * q^((2*n-1)^2) ) [_Joerg Arndt, _, Mar 04 2010]
STATUS
proposed
editing
STATUS
editing
proposed
EXAMPLE
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
EXAMPLE
I define a divisor d|n to be inferior if d <= n/d, so a(n) is the number of inferior odd divisors of n. These divisors for selected n are the columns below:
The inferior odd divisors for selected n are the columns below:
EXAMPLE
From Gus Wiseman, Feb 11 2021: (Start)
I define a divisor d|n to be inferior if d <= n/d, so a(n) is the number of inferior odd divisors of n. These 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)
CROSSREFS
Cf. A001227, A000005, A000196, A001227, A069289, A182469.
Positions of first appearances are A334853.
A055396 selects the least prime index.
A061395 selects the greatest prime index.
A340653 counts balanced factorizations.
- Odd -
A000009 counts partitions into odd parts (A066208).
A024429 counts set partitions of odd length.
A026424 lists numbers with odd Omega.
A027193 counts odd-length partitions.
A067659 counts strict partitions of odd length (A030059).
A340692 counts partitions of odd rank.
- 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.
Cf. A000196, A182469, A001227A001055, ~A058695, ~A160786, A244991, A300272, A340101, A340607, ~A340654, ~A340655, ~A340656/~A340657, A340832, ~A340854/~A340855, A340931.
STATUS
approved
editing
STATUS
editing
approved