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Numbers n for which n=(n'' mod n'), where n' and n'' are the first and second arithmetic derivative of n.
1

%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