A357428 Numbers whose digit representation in base 2 is equal to the digit representation in base 2 of the initial terms of their sets of divisors in increasing order.

1, 6, 52, 63, 222, 2037, 6776, 26896, 124641, 220336192, 222066488

Offset: 1

Author

Michel Marcus, Sep 28 2022

Keywords

• nonn
• base
• more

Comments

a(1), a(2), a(3), a(8) and a(10) belong to A164894; A164894(13) = 2032242676629600594233921536, A164894(19) = 1288086824419468350412109535086131006200927555108489920512 and A164894(29) are also terms. - Rémy Sigrist, Sep 28 2022

Examples

			In base 2, 6 is 110 and its first divisors are 1 and 2, that is, 1 and 10.
		

Crossrefs

Cf. A164894, A175252 (base 10), A357429 (base 3).

Programs

PARI

isok(k) = my(s=[]); fordiv(k, d, s=concat(s, binary(d)); if (fromdigits(s, 2)==k, return(1)); if (fromdigits(s,2)> k, return(0)));

Python

from sympy import divisors
def ok(n):
    target, s = bin(n)[2:], ""
    if target[0] != "1": return False
    for d in divisors(n):
        s += bin(d)[2:]
        if len(s) >= len(target): return s == target
        elif not target.startswith(s): return False
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Oct 01 2022

Extensions

a(10)-a(11) from Rémy Sigrist, Sep 28 2022