%I #12 Jun 25 2012 06:13:13
%S 16,20,64,108,135,164,352,432,729,1024,1107,2376,2916,6912,12500,
%T 15625,16038,16384,19683,43692,46656,47616,50000,84375,110592,128125,
%U 188228,275000,294921,314928,321408,337500,746496,800000,1270539,1856250
%N Numbers n for which n=(n'' mod n'), where n' and n'' are the first and second arithmetic derivative of n.
%e n=432, n'=1296, n''=4320 and 4320=1296*3+432.
%p with(numtheory);
%p A213241:= proc(i)
%p local a,b,n,p,pfs;
%p for n from 1 to i do
%p pfs:=ifactors(n)[2]; a:=n*add(op(2,p)/op(1,p),p=pfs);
%p pfs:=ifactors(a)[2]; b:=a*add(op(2,p)/op(1,p),p=pfs);
%p pfs:=ifactors(b)[2]; c:=b*add(op(2,p)/op(1,p),p=pfs);
%p if a>0 then if (b mod a)=n then print(n); fi; fi;
%p od;
%p end:
%p A213241(10000000);
%Y Cf. A003415
%K nonn
%O 1,1
%A _Paolo P. Lava_, Jun 12 2012