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A213240 Numbers n such that sum of digits of n = sum of digits of n’, where n’ is the arithmetic derivative of n.

%I A213240 #18 Jun 15 2012 19:40:52
%S A213240 4,22,27,54,56,81,94,108,121,135,166,202,216,243,245,260,265,266,272,
%T A213240 274,308,344,346,355,382,405,445,454,459,513,517,518,526,562,567,594,
%U A213240 634,648,675,702,706,729,784,806,832,837,841,891,913,920,922,945,950,972
%N A213240 Numbers n such that sum of digits of n = sum of digits of n’, where n’ is the arithmetic derivative of n.
%H A213240 Paolo P. Lava, <a href="/A213240/b213240.txt">Table of n, a(n) for n = 1..10000</a>
%e A213240 n=344 and 3+4+4=11; n’=524 and 5+2+4=11.
%p A213240 with(numtheory);
%p A213240 A213240:=proc(q)
%p A213240 local a,b,d,n,p,pfs;
%p A213240 for n from 1 to q do
%p A213240   pfs:=ifactors(n)[2]; a:=n*add(op(2,p)/op(1,p),p=pfs); b:=0;
%p A213240   while a>0 do b:=b+(a mod 10); a:=trunc(a/10); od;
%p A213240   a:=n; d:=0; while a>0 do d:=d+(a mod 10); a:=trunc(a/10); od;
%p A213240   if b=d then print(n); fi;
%p A213240 od; end:
%p A213240 A213240(100000000);
%Y A213240 Cf. A003415, A006753, A213239
%K A213240 nonn,base
%O A213240 1,1
%A A213240 _Paolo P. Lava_, Jun 07 2012