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Numbers n such that sum of digits of n = sum of digits of anti-divisors of n.
2

%I #25 Dec 07 2019 12:18:26

%S 5,8,64,691,1779,2851,6361,9066,9606,9771,10789,10996,18996,21481,

%T 22569,27529,27691,31516,36709,36776,42649,48651,53296,56586,58749,

%U 60369,64794,72889,76754,78766,79374,79896,80989,86596,90606,90879,92766,96171,98979,108529

%N Numbers n such that sum of digits of n = sum of digits of anti-divisors of n.

%e Sum of digits of 1779 is 1+7+7+9=24.

%e Anti-divisors of 1779 are 2, 6, 1186 and their digits’ sum is 2+6+1+1+8+6=24.

%p with(numtheory);

%p A213239:=proc(q)

%p local a,b,c,d,k,n;

%p for n from 1 to q do

%p a:=0; b:=0;

%p for k from 2 to n-1 do

%p if abs((n mod k)-k/2)<1 then

%p c:=k; while c>0 do b:=b+(c mod 10); c:=trunc(c/10); od; fi; od;

%p c:=n; d:=0; while c>0 do d:=d+(c mod 10); c:=trunc(c/10); od;

%p if b=d then print(n); fi; od; end:

%p A213239(100000);

%o (Python)

%o [n for n in range(1,10**5) if sum([sum([int(x) for x in str(d)]) for d in range(2,n) if n % d and 2*n % d in [d-1,0,1]]) == sum([int(x) for x in str(n)])] # _Chai Wah Wu_, Aug 08 2014

%Y Cf. A006753, A066417, A213240.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Jun 07 2012