A230165 Numbers k such that k = sigma(k'), where k' is the arithmetic derivative of k.

6, 15, 42, 47058

Offset: 1

Author

Paolo P. Lava, Oct 14 2013

Keywords

• nonn
• more

Comments

a(5) > 10^10. - Giovanni Resta, Oct 14 2013

Terms of this sequence and A342021 group into pairs (m, m'), where m is a term of this sequence and m' is a term of A342021. - Max Alekseyev, Feb 13 2025

Examples

			Arithmetic derivative of 15 is 8 and sigma(8) = 15.
		

Crossrefs

Cf. A003415, A229342, A230164, A342021.

Programs

Maple

with(numtheory); P:=proc(q) local n; for n from 1 to q do
if n=sigma(n*add(op(2,p)/op(1,p),p=ifactors(n)[2])) then print(n);
fi; od; end: P(10^9);

Formula

a(n) = sigma(A342021(n)). - Max Alekseyev, Feb 13 2025