A241214 Solutions of the equation (n+2)' = (n+1)' + n', where n' is the arithmetic derivative of n.

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

Links

Table of n, a(n) for n=1..10.

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

Adjacent sequences: A241211 A241212 A241213 * A241215 A241216 A241217

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