A319801 Odd numbers without middle divisors.

3, 5, 7, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 75, 79, 83, 85, 87, 89, 93, 95, 97, 101, 103, 105, 107, 109, 111, 113, 115, 119, 123, 125, 127, 129, 131, 133, 137, 139, 141, 145, 147, 149, 151, 155, 157, 159, 161, 163, 167, 171, 173, 175, 177

Offset

1,1

Comments

Odd numbers k such that the symmetric representation of sigma(k) has an even number of parts.

All odd primes (A065091) are in the sequence.

For the definition of middle divisors, see A067742.

For more information about the symmetric representation of sigma(k) see A237593.

Links

Table of n, a(n) for n=1..70.

Example

21 is in the sequence because it's an odd number and the symmetric representation of sigma(21) = 32 has an even number of parts (more exactly four parts), as shown below:
.     _ _ _ _ _ _ _ _ _ _ _ 11
.    |_ _ _ _ _ _ _ _ _ _ _|
.                          |
.                          |
.                          |_ _ _ 5
.                          |_ _  |_
.                              |_ _|_
.                                  | |_ 5
.                                  |_  |
.                                    | |
.                                    |_|_ _ _ _ 11
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            |_|
.

Crossrefs

Intersection of A005408 and A071561.

Cf. A000203, A065091, A067742, A071090, A071562, A236104, A237270, A237271, A237593, A239931, A239933, A240542, A245092, A280919, A281007, A296508, A299761, A299777, A303297, A319529, A319796, A319802.

Sequence in context: A250094 A351398 A285516 * A339907 A255602 A319181

Adjacent sequences: A319798 A319799 A319800 * A319802 A319803 A319804

Keyword

nonn

Author

Omar E. Pol, Sep 28 2018

Status

approved