A368341 Fixed points of A368207.

0, 1, 2, 8, 9, 32, 128, 238, 512, 1012, 2048, 8192, 15070, 21658, 32768, 131072, 383548, 391612, 524288

Offset: 1

Author

Chai Wah Wu, Dec 21 2023

Keywords

• nonn
• more

Comments

Numbers k such that A368207(k)=k.

Conjecture: 2^(2k+1) for k>=0 (A004171) are terms.

Crossrefs

Cf. A004171, A368207.

Programs

Python

from itertools import count, islice
from sympy import divisors
def A368341_gen(startvalue=0): # generator of terms >= startvalue
    for n in count(max(startvalue,0)):
        c = 0
        for d2 in divisors(n):
            if d2**2 > n:
                break
            c += (d2<<2)-2 if d2**2n:
                break
        if c<=n:
            for wx in range(1,(n>>1)+1):
                for d1 in divisors(wx):
                    if d1**2 > wx:
                        break
                    for d2 in divisors(m:=n-wx):
                        if d2**2 > m:
                            break
                        if wx < d1*d2:
                            k = 1
                            if d1**2 != wx:
                                k <<=1
                            if d2**2 != m:
                                k <<=1
                            c+=k
                            if c>n:
                                break
        if c==n:
            yield n
A368341_list = list(islice(A368341_gen(),10))

Extensions

a(17)-a(19) from Chai Wah Wu, Dec 22 2023