A376299 - OEIS

%I #24 Oct 19 2024 08:33:57

%S 1,4,90,120

%N Fixed points of A008473.

%C These are the numbers such that the sum of the powerfree parts of the divisors of n equals n.

%C These fixed points appeared in A299352 and the linked Combo Class video. The former notes there are no more fixed points <= 10^8. - _Michael S. Branicky_, Sep 19 2024

%C Any further terms are > 10^11. - _Lucas A. Brown_, Oct 19 2024

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A376299.py">Python program</a>.

%H Combo Class, <a href="https://www.youtube.com/watch?v=pylw9t4j6bM">The Mysterious Pattern I Found Within Prime Factorizations</a>, Sep 12 2024.

%o (Python)

%o from sympy import factorint, prod

%o A008473 = lambda n: prod(sum(pk) for pk in factorint(n).items())

%o isok = lambda n: A008473(n) == n

%o print([n for n in range(1, 10**6) if isok(n)])

%Y Cf. A008473, A299352.

%K nonn,more,hard

%O 1,2

%A _Darío Clavijo_, Sep 19 2024