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A241214
Solutions of the equation (n+2)' = (n+1)' + n', where n' is the arithmetic derivative of n.
0
1, 4, 20257, 43910, 563101, 18895033, 119847146, 305478634708, 7461770367940, 29820549118362
OFFSET
1,2
COMMENTS
a(9) > 5*10^11. - Giovanni Resta, Apr 18 2014
a(11) > 5*10^13. - Hiroaki Yamanouchi, Aug 27 2015
EXAMPLE
The arithmetic derivative of 43910+2 is 69948, of 43910+1 is 39201, of 43910 is 30747 and 69948 = 39201 + 30747.
MAPLE
with(numtheory); P:= proc(q) local a, b, c, n, p;
for n from 1 to q do
a:=(n+2)*add(op(2, p)/op(1, p), p=ifactors(n+2)[2]);
b:=(n+1)*add(op(2, p)/op(1, p), p=ifactors(n+1)[2]);
c:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);
if a=b+c then print(n); fi; od; end: P(10^9);
CROSSREFS
Cf. A003415.
Sequence in context: A053015 A089210 A203037 * A034014 A217600 A275684
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Apr 17 2014
EXTENSIONS
a(7)-a(8) from Giovanni Resta, Apr 18 2014
a(9)-a(10) from Hiroaki Yamanouchi, Aug 27 2015
STATUS
approved