A276701 Numbers n>0 such that n’ = (n-1)’ + (n-2)’, where n’ is the arithmetic derivative of n.

1, 3, 6, 20259, 43912, 563103, 18895035, 119847148, 305478634710

Offset

1,2

Comments

a(10) > 5*10^12. - Giovanni Resta, Sep 16 2016

Links

Table of n, a(n) for n=1..9.

Example

6’ = 5, 5’ = 1, 4’ = 4 and 5 = 1 + 4.

Maple

with(numtheory): P:= proc(q) local a, b, c, n, p;
a:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);
b:=(n-1)*add(op(2, p)/op(1, p), p=ifactors(n-1)[2]);
c:=(n-2)*add(op(2, p)/op(1, p), p=ifactors(n-2)[2]);
if a=b+c then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A003415.

Sequence in context: A134901 A157564 A122182 * A157596 A111316 A297530

Adjacent sequences: A276698 A276699 A276700 * A276702 A276703 A276704

Keyword

nonn,more

Author

Paolo P. Lava, Sep 15 2016

Extensions

a(9) from Giovanni Resta, Sep 16 2016

Status

approved