A227502 Numbers n such that Sum_{i=1..n} i^(i') == 0 (mod n), where i' is the arithmetic derivative of i.

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

Offset

1,2

Comments

a(14) > 200000. - Giovanni Resta, Jul 15 2013

a(15) > 1000000. - Bert Dobbelaere, Dec 24 2018

Links

Table of n, a(n) for n=1..14.

Example

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

Maple

with(numtheory); ListA227502:=proc(q)  local a, n, p;  a:=0;
for n from 1 to q do a:=a+n^(n*add(op(2, p)/op(1, p), p=ifactors(n)[2]));
if a mod n=0 then print(n);  fi; od; end: ListA227502(10^6);

Mathematica

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 *)

Crossrefs

Cf. A003415, A227848.

Sequence in context: A145039 A112633 A113916 * A268065 A049490 A112391

Adjacent sequences: A227499 A227500 A227501 * A227503 A227504 A227505

Keyword

nonn,more

Author

Paolo P. Lava, Jul 13 2013

Extensions

a(13) from Giovanni Resta, Jul 15 2013

a(14) from Bert Dobbelaere, Dec 24 2018

Status

approved