A379169 Let m be 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
Examples
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.
Programs
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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);
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Mathematica
A379169Q[k_] := Divisible[FromDigits[StringJoin[IntegerString[Divisors[k], 2]], 2], k]; Select[Range[50000], A379169Q] (* Paolo Xausa, Jan 29 2025 *)
Comments