A319802 Even numbers without middle divisors.

10, 14, 22, 26, 34, 38, 44, 46, 52, 58, 62, 68, 74, 76, 78, 82, 86, 92, 94, 102, 106, 114, 116, 118, 122, 124, 134, 136, 138, 142, 146, 148, 152, 158, 164, 166, 172, 174, 178, 184, 186, 188, 194, 202, 206, 212, 214, 218, 222, 226, 230, 232, 236, 244, 246, 248, 250, 254, 258, 262, 268, 274, 278, 282, 284

Offset

1,1

Comments

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

For the definition of middle divisors, see A067742.

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

Let p be a prime > 5. Then a(n) is a number of the form m*p where m is an even number < sqrt(p). - David A. Corneth, Sep 28 2018

First differs from A244894 at a(51) = 230. - R. J. Mathar, Oct 04 2018

Is this twice A101550? - Omar E. Pol, Oct 04 2018

This sequence is not twice A101550: first differs at a(57) = 250 != 254 = 2*A101550(57). - Michael S. Branicky, Oct 14 2021

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

10 is in the sequence because it's an even number and the symmetric representation of sigma(10) = 18 has an even number of parts as shown below:
.
.     _ _ _ _ _ _ 9
.    |_ _ _ _ _  |
.              | |_
.              |_ _|_
.                  | |_ _ 9
.                  |_ _  |
.                      | |
.                      | |
.                      | |
.                      | |
.                      |_|
.

Prog

(Python)
from sympy import divisors
def ok(n):
    if n < 2 or n%2 == 1: return False
    return not any(n//2 <= d*d < 2*n for d in divisors(n, generator=True))
print(list(filter(ok, range(285)))) # Michael S. Branicky, Oct 14 2021

Crossrefs

Intersection of A005843 and A071561.

Cf. A244894 (a subsequence).

Cf. A000203, A067742, A071090, A071562, A236104, A237270, A237271, A237593, A239932, A239934, A240542, A245092, A280919, A281007, A296508, A299761, A299777, A303297, A319529, A319796, A319801.

Sequence in context: A063764 A253569 A138511 * A244894 A167611 A151740

Adjacent sequences: A319799 A319800 A319801 * A319803 A319804 A319805

Keyword

nonn

Author

Omar E. Pol, Sep 28 2018

Status

approved