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A342082
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Numbers with an inferior odd divisor > 1.
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2
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9, 12, 15, 18, 21, 24, 25, 27, 30, 33, 35, 36, 39, 40, 42, 45, 48, 49, 50, 51, 54, 55, 56, 57, 60, 63, 65, 66, 69, 70, 72, 75, 77, 78, 80, 81, 84, 85, 87, 90, 91, 93, 95, 96, 98, 99, 100, 102, 105, 108, 110, 111, 112, 114, 115, 117, 119, 120, 121, 123, 125
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OFFSET
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1,1
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COMMENTS
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We define a divisor d|n to be inferior if d <= n/d. Inferior divisors are counted by A038548 and listed by A161906.
Numbers n with an odd prime factor <= sqrt(n). - Chai Wah Wu, Mar 09 2021
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LINKS
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EXAMPLE
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The divisors > 1 of 72 are {2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72}, of which {3, 9} are odd and {2, 3, 4, 6, 8} are inferior, with intersection {3}, so 72 is in the sequence.
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MATHEMATICA
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Select[Range[100], Function[n, Select[Divisors[n]//Rest, OddQ[#]&&#<=n/#&]!={}]]
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PROG
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(Python)
from sympy import primefactors
A342082_list = [n for n in range(1, 10**3) if len([p for p in primefactors(n) if p > 2 and p*p <= n]) > 0] # Chai Wah Wu, Mar 09 2021
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CROSSREFS
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The strictly inferior version is the same with A001248 removed.
A006530 selects the greatest prime factor.
A020639 selects the smallest prime factor.
A038548 counts superior (or inferior) divisors, with strict case A056924.
- Odd -
A026424 lists numbers with odd Omega.
A027193 counts odd-length partitions.
A058695 counts partitions of odd numbers.
A340101 counts factorizations into odd factors; A340102 also has odd length.
A341594 counts strictly superior odd divisors
A341675 counts superior odd divisors.
Cf. A000005, A000203, A001055, A001221, A001222, A001414, A207375, A244991, A300272, A340832, A340931.
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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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