cp's OEIS Frontend

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.

%I A379169 #12 Aug 12 2025 11:39:34
%S A379169 1,2,4,6,8,16,21,32,48,52,56,64,99,110,128,168,198,256,336,384,512,
%T A379169 656,960,1024,1376,1792,1820,1953,2048,3072,3456,3744,4096,4270,4448,
%U A379169 4601,4672,6526,8192,8704,11144,11264,12800,13684,16384,19712,24576,32768,37116
%N 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.
%C A379169 Powers of 2 are part of the sequence.
%e A379169 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.
%p A379169 with(numtheory): P:=proc(q) global a,b,c,k,n,v; v:=[];
%p A379169 for n from 1 to q do a:=sort([op(divisors(n))]); b:=0;
%p A379169 for k from 1 to nops(a) do c:=convert(a[k],binary,decimal); b:=b*10^length(c)+c; od;
%p A379169 if frac(convert(b,decimal,binary)/n)=0 then v:=[op(v),n]; fi;
%p A379169 op(v); od; end: P(37116);
%t A379169 A379169Q[k_] := Divisible[FromDigits[StringJoin[IntegerString[Divisors[k], 2]], 2], k];
%t A379169 Select[Range[50000], A379169Q] (* _Paolo Xausa_, Jan 29 2025 *)
%Y A379169 Cf. A000079, A069872, A379170.
%K A379169 nonn,easy,base
%O A379169 1,2
%A A379169 _Paolo P. Lava_, Dec 17 2024