A230541 - OEIS

%I #11 Oct 24 2013 12:04:14

%S 11,20,22,26,33,65,82,117,209,218,376,417,483,508,537,561,675,758,910,

%T 1186,1208,1317,1350,1828,2039,2192,2347,2471,2840,2889,4129,4369,

%U 4389,4495,4893,5007,6430,7276,7690,8246,8777,9289,10651,11727,11797,12048,12099

%N 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 Paolo P. Lava, <a href="/A230541/b230541.txt">Table of n, a(n) for n = 1..100</a>

%e 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 Therefore 376 is part of the sequence because the digits of 720 are a permutation of the digits of 270.

%p with(numtheory); P:= proc(i) local a,b,c,j,k,n,ok,p;

%p for n from 3 to i do b:=[]; c:=[];

%p k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od;

%p a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;

%p while a>0 do b:=[op(b),a mod 10]; a:=trunc(a/10); od; a:=sigma(n);

%p while a>0 do c:=[op(c),a mod 10]; a:=trunc(a/10); od;

%p if nops(b)=nops(c) then b:=sort(b); c:=sort(c); b:=b-c; ok:=1;

%p for j from 1 to nops(b) do if b[j]<>0  then ok:=0; break; fi; od;

%p if ok=1 then print(n); fi; fi; od; end; P(10^6);

%Y Cf. A000203, A066417, A115920.

%K nonn,base,less

%O 1,1

%A _Paolo P. Lava_, Oct 23 2013