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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).

%I A230541 #11 Oct 24 2013 12:04:14
%S A230541 11,20,22,26,33,65,82,117,209,218,376,417,483,508,537,561,675,758,910,
%T A230541 1186,1208,1317,1350,1828,2039,2192,2347,2471,2840,2889,4129,4369,
%U A230541 4389,4495,4893,5007,6430,7276,7690,8246,8777,9289,10651,11727,11797,12048,12099
%N 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).
%H A230541 Paolo P. Lava, <a href="/A230541/b230541.txt">Table of n, a(n) for n = 1..100</a>
%e A230541 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.
%e A230541 Therefore 376 is part of the sequence because the digits of 720 are a permutation of the digits of 270.
%p A230541 with(numtheory); P:= proc(i) local a,b,c,j,k,n,ok,p;
%p A230541 for n from 3 to i do b:=[]; c:=[];
%p A230541 k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p A230541 a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
%p A230541 while a>0 do b:=[op(b),a mod 10]; a:=trunc(a/10); od; a:=sigma(n);
%p A230541 while a>0 do c:=[op(c),a mod 10]; a:=trunc(a/10); od;
%p A230541 if nops(b)=nops(c) then b:=sort(b); c:=sort(c); b:=b-c; ok:=1;
%p A230541 for j from 1 to nops(b) do if b[j]<>0  then ok:=0; break; fi; od;
%p A230541 if ok=1 then print(n); fi; fi; od; end; P(10^6);
%Y A230541 Cf. A000203, A066417, A115920.
%K A230541 nonn,base,less
%O A230541 1,1
%A A230541 _Paolo P. Lava_, Oct 23 2013