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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 16 04:54 EDT 2019. Contains 324145 sequences. (Running on oeis4.)