A230541 Numbers n such that the digits of sigma(n) are a permutation of those of sigma*(n), where sigma*(n) is the sum of anti-divisors of n (A066417).

11, 20, 22, 26, 33, 65, 82, 117, 209, 218, 376, 417, 483, 508, 537, 561, 675, 758, 910, 1186, 1208, 1317, 1350, 1828, 2039, 2192, 2347, 2471, 2840, 2889, 4129, 4369, 4389, 4495, 4893, 5007, 6430, 7276, 7690, 8246, 8777, 9289, 10651, 11727, 11797, 12048, 12099

Offset: 1

Author

Paolo P. Lava, Oct 23 2013

Keywords

• nonn
• base
• less

Examples

			Divisors of 376 are 1, 2, 4, 8, 47, 94, 376, 188 and sigma(376) = 720; anti-divisors of 376 are 3, 16, 251 and sigma*(376) = 270.
Therefore 376 is part of the sequence because the digits of 720 are a permutation of the digits of 270.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000203, A066417, A115920.

Programs

Maple

with(numtheory); P:= proc(i) local a,b,c,j,k,n,ok,p;
for n from 3 to i do b:=[]; c:=[];
k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od;
a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
while a>0 do b:=[op(b),a mod 10]; a:=trunc(a/10); od; a:=sigma(n);
while a>0 do c:=[op(c),a mod 10]; a:=trunc(a/10); od;
if nops(b)=nops(c) then b:=sort(b); c:=sort(c); b:=b-c; ok:=1;
for j from 1 to nops(b) do if b[j]<>0  then ok:=0; break; fi; od;
if ok=1 then print(n); fi; fi; od; end; P(10^6);