A379169 Let m the concatenation, in ascending order, of the divisors of k written in base 2 and then converted to base 10. Sequence lists k which divide m.

1, 2, 4, 6, 8, 16, 21, 32, 48, 52, 56, 64, 99, 110, 128, 168, 198, 256, 336, 384, 512, 656, 960, 1024, 1376, 1792, 1820, 1953, 2048, 3072, 3456, 3744, 4096, 4270, 4448, 4601, 4672, 6526, 8192, 8704, 11144, 11264, 12800, 13684, 16384, 19712, 24576, 32768, 37116

Offset

1,2

Comments

Powers of 2 are part of the sequence.

Links

Table of n, a(n) for n=1..49.

Example

Divisors of 6 are 1, 2, 3, 6, which in base 2 are 1, 10, 11, 110. Their concatenation is 11011110 which in base 10 is 222. Finally 222/6 = 37 is an integer, so 6 is a member of the sequence.

Maple

with(numtheory): P:=proc(q) global a, b, c, k, n, v; v:=[];
for n from 1 to q do a:=sort([op(divisors(n))]); b:=0;
for k from 1 to nops(a) do c:=convert(a[k], binary, decimal); b:=b*10^length(c)+c; od;
if frac(convert(b, decimal, binary)/n)=0 then v:=[op(v), n]; fi;
op(v); od; end: P(37116);

Mathematica

A379169Q[k_] := Divisible[FromDigits[StringJoin[IntegerString[Divisors[k], 2]], 2], k];
Select[Range[50000], A379169Q] (* Paolo Xausa, Jan 29 2025 *)

Crossrefs

Cf. A000079, A069872, A379170.

Sequence in context: A364814 A353867 A356956 * A064408 A316225 A100685

Adjacent sequences: A379165 A379166 A379167 * A379170 A379171 A379172

Keyword

nonn,easy,base,changed

Author

Paolo P. Lava, Dec 17 2024

Status

approved