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

1,2

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

Links

Table of n, a(n) for n=1..11.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A271680 A165896 A080265 * A292053 A202925 A287082

Adjacent sequences: A357425 A357426 A357427 * A357429 A357430 A357431

Keyword

nonn,base,more

Author

Michel Marcus, Sep 28 2022

Extensions

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

Status

approved