

A342082


Numbers with an inferior odd divisor > 1.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

We define a divisor dn 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


LINKS

Table of n, a(n) for n=1..61.


EXAMPLE

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.


MATHEMATICA

Select[Range[100], Function[n, Select[Divisors[n]//Rest, OddQ[#]&&#<=n/#&]!={}]]


PROG

(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


CROSSREFS

The strictly inferior version is the same with A001248 removed.
Positions of terms > 1 in A069288.
The superior version is A116882, with complement A116883.
The complement is A342081.
A006530 selects the greatest prime factor.
A020639 selects the smallest prime factor.
A038548 counts superior (or inferior) divisors, with strict case A056924.
 Odd 
A000009 counts partitions into odd parts, ranked by A066208.
A001227 counts odd divisors.
A026424 lists numbers with odd Omega.
A027193 counts oddlength partitions.
A058695 counts partitions of odd numbers.
A067659 counts strict partitions of odd length, ranked by A030059.
A340101 counts factorizations into odd factors; A340102 also has odd length.
A340854/A340855 cannot/can be factored with odd minimum factor.
A341594 counts strictly superior odd divisors
A341675 counts superior odd divisors.
 Inferior: A033676, A066839, A161906.
 Superior: A033677, A051283, A059172, A063538/A063539.
 Strictly Inferior A333805, A341674.
 Strictly Superior: A064052/A048098, A341645/A341646.
Cf. A000005, A000203, A001055, A001221, A001222, A001414, A207375, A244991, A300272, A340832, A340931.
Sequence in context: A119486 A235341 A356333 * A161345 A102655 A308748
Adjacent sequences: A342079 A342080 A342081 * A342083 A342084 A342085


KEYWORD

nonn


AUTHOR

Gus Wiseman, Mar 06 2021


STATUS

approved



