A278439 -id:A278439 - cp's OEIS frontend

A278440 Numbers n such that A244112(n) | n.

22, 777, 4444, 68868, 200000, 303030, 333000, 333333, 555555, 660000, 660660, 666666, 700000, 2332200, 3131313, 4444400, 6060600, 7007000, 7700000, 9009790, 9656955, 9885585, 11517771, 14233221, 14331231, 14333110, 14411040, 15143331, 15233221, 15331231, 15333110

Offset: 1

Paolo P. Lava, Nov 25 2016

A244112(68868) = 3826 and 68868 / 3826 = 18.

Paolo P. Lava, Table of n, a(n) for n = 1..200

Cf. A237605, A244112, A278439, A278441.

with(numtheory): P:=proc(q) local a,b,c,d,j,k,n; for n from 1 to q do a:=sort(convert(n,base,10));
for k from 1 to trunc(nops(a)/2) do c:=a[k]; a[k]:=a[nops(a)-k+1]; a[nops(a)-k+1]:=c; od;  k:=1; b:=a[1]; c:=0;
for j from 2 to nops(a) do if a[j]=b then k:=k+1; else d:=10*k+b; c:=c*10^(ilog10(d)+1)+d; k:=1; b:=a[j]; fi; od;
d:=10*k+b; c:=c*10^(ilog10(d)+1)+d; if type(n/c,integer) then print(n); fi; od; end: P(10^99);

Select[Range[10^6], Divisible[#, FromDigits@ Flatten@ Map[IntegerDigits, DeleteCases[#, k_ /; First@ k == 0]] &@ Reverse@ MapIndexed[{#1, (First@ #2 - 1)} &, RotateRight@ DigitCount@ #]] &] (* Michael De Vlieger, Dec 12 2016 *)

A278441 Numbers n such that n | A244112(n).

Original entry on oeis.org

1, 2, 5, 10, 22, 26, 32, 62, 91, 330, 370, 519, 575, 710, 1060, 4055, 29377, 79554, 108690, 150320, 306440, 2510048, 3605570, 14233221, 14331231, 14333110, 14509410, 15143331, 15233221, 15331231, 15333110, 16143331, 16153331, 16233221, 16331231, 16333110, 17143331

Offset: 1

Paolo P. Lava, Nov 25 2016

The sequence is bounded. See comment in A278439.

			A244112(519) = 191511 and 191511 / 519 = 369.

Paolo P. Lava, List of terms and corresponding ratios for n <= 10^9.

Cf. A237605, A244112, A278439, A278440.

with(numtheory): P:=proc(q) local a,b,c,d,j,k,n; for n from 1 to q do a:=sort(convert(n,base,10));
for k from 1 to trunc(nops(a)/2) do c:=a[k]; a[k]:=a[nops(a)-k+1]; a[nops(a)-k+1]:=c; od;  k:=1; b:=a[1]; c:=0;
for j from 2 to nops(a) do if a[j]=b then k:=k+1; else d:=10*k+b; c:=c*10^(ilog10(d)+1)+d; k:=1; b:=a[j]; fi; od;
d:=10*k+b; c:=c*10^(ilog10(d)+1)+d; if type(c/n,integer) then print(n); fi; od; end: P(10^99);

cp's OEIS Frontend

A278440 Numbers n such that A244112(n) | n.

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