A227502 - OEIS

%I #20 Dec 26 2018 10:47:04

%S 1,3,7,19,32,57,99,103,439,540,2656,18156,179171,235056

%N Numbers n such that Sum_{i=1..n} i^(i') == 0 (mod n), where i' is the arithmetic derivative of i.

%C a(14) > 200000. - _Giovanni Resta_, Jul 15 2013

%C a(15) > 1000000. - _Bert Dobbelaere_, Dec 24 2018

%e 1^1' + 2^2' + 3^3' = 1^0 + 2^1 + 3^1 = 6 and 6 == 0 (mod 3).

%p with(numtheory); ListA227502:=proc(q)  local a,n,p;  a:=0;

%p for n from 1 to q do a:=a+n^(n*add(op(2,p)/op(1,p),p=ifactors(n)[2]));

%p if a mod n=0 then print(n);  fi; od; end: ListA227502(10^6);

%t d[n_] := d[n] = n*Total[Apply[#2/#1 &, FactorInteger[n], {1}]]; Reap[For[n = 1, n <= 2*10^5, n++, If[Mod[Sum[k^d[k], {k, 1, n}], n] == 0, Print[n]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Feb 21 2014 *)

%Y Cf. A003415, A227848.

%K nonn,more

%O 1,2

%A _Paolo P. Lava_, Jul 13 2013

%E a(13) from _Giovanni Resta_, Jul 15 2013

%E a(14) from _Bert Dobbelaere_, Dec 24 2018