A069872 -id:A069872 - 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.

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

Paolo P. Lava, Dec 17 2024

Powers of 2 are part of the sequence.

			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.

Cf. A000079, A069872, A379170.

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);

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

A249765 Numbers that divide the concatenation, in descending order, of their anti-divisors.

Original entry on oeis.org

7, 23957, 56483, 74651, 316782, 13594764, 14473747, 30056837

Offset: 1

Paolo P. Lava, Nov 06 2014

			Anti-divisors of 7 are and 2, 3, 5 and their concatenation in descending order is 532. Finally, 532 / 7 = 76.

Cf. A066272, A069872, A224930, A240265, A249764.

P:=proc(q) local a,k,n; for n from 3 to q do a:=0;
for k from n-1 by -1 to 2 do if abs((n mod k)-k/2)<1 then a:=a*10^(ilog10(k)+1)+k; fi; od;
if type(a/n,integer) then print(n); fi; od; end: P(10^9);

a(5)-a(8) from Chai Wah Wu, Nov 21 2014

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.

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