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A227848
Numbers n such that Sum_{i=1..n} (i')^i == 0 (mod n), where i' is the arithmetic derivative of i.
9
1, 9, 71, 120, 331, 393, 728, 1223, 3697, 4123, 6791, 7391, 23911, 25099, 35287, 86442, 86716, 118034, 292411, 352970, 527255, 606425
OFFSET
1,2
COMMENTS
a(19) > 200000. - Giovanni Resta, Aug 01 2013
EXAMPLE
1'^1 + 2'^2 + 3'^3 + 4'^4 + 5'^5 + 6'^6 + 7'^7 + 8'^8 + 9'^9 = 0^1 + 1^2 + 1^3 + 4^4 + 1^5 + 5^6 + 1^7 + 12^8 + 6^9 = 440075277 and 440075277 / 9 = 48897253.
MAPLE
with(numtheory); ListA227848:=proc(q) local a, n, p; a:=0;
for n from 1 to q do a:=a+(n*add(op(2, p)/op(1, p), p=ifactors(n)[2]))^n;
if a mod n=0 then print(n); fi; od; end: ListA227848(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[d[k]^k, {k, 1, n}], n] == 0, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Feb 21 2014 *)
CROSSREFS
Sequence in context: A226013 A156705 A231419 * A226846 A226711 A231420
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Aug 01 2013
EXTENSIONS
a(16)-a(18) from Giovanni Resta, Aug 01 2013
a(19)-a(22) from Bert Dobbelaere, Dec 23 2018
STATUS
approved