A045817 Numbers n written in base 7, where in the list of divisors of n (in base 7), each digit 0-6 appears equally often.

3602, 246506, 264533, 266405, 303652, 320556, 324255, 325605, 342560, 345064, 345406, 345604, 346340, 362055, 414056, 430462, 434630, 435065, 436430, 436550, 453605, 500426, 500641, 506022, 524360, 524406, 526433, 530632, 532650, 533402

Offset: 1

Author

Naohiro Nomoto

Keywords

• easy
• nonn
• base

Examples

			E.g., divisors of 342560 (base 7) are (1,2,10,20,15463,34256,154630,342560) (all in base 7); the numbers of digits (0-6) are [0(4),1(4),2(4),3(4),4(4),5(4),6(4)].
		

Links

• Robert Israel, Table of n, a(n) for n = 1..161
• N. Nomoto, In the list of divisors of n,... [broken link]

Crossrefs

Cf. A038564, A038565, A045818.

Programs

Maple

N:= 7^6:
cv7:= proc(n) local L; L:= convert(n,base,7);
add(L[i]*10^(i-1),i=1..nops(L)) end proc:
V:= Matrix(N,7,datatype=integer[8]):
count:= 0: Res:= NULL:
for i from 1 to N do
  L:= convert(i,base,7);
  M:= Vector[row]([seq(numboccur(d,L),d=0..6)],datatype=integer[8]);
  for r from i to N by i do V[r,..]:= V[r,..] + M od;
  if nops(convert(V[i,..],set))=1 then
    count:= count+1;
    w:= cv7(i);
    Res:= Res,w;
  fi
od:
Res; # Robert Israel, Sep 07 2018

Extensions

Definition clarified by Robert Israel, Sep 07 2018