A376299 Fixed points of A008473.

1, 4, 90, 120

Offset: 1

Author

Darío Clavijo, Sep 19 2024

Keywords

• nonn
• more
• hard

Comments

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

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

Any further terms are > 10^11. - Lucas A. Brown, Oct 19 2024

Links

• Lucas A. Brown, Python program.
• Combo Class, The Mysterious Pattern I Found Within Prime Factorizations, Sep 12 2024.

Crossrefs

Cf. A008473, A299352.

Programs

Python

from sympy import factorint, prod
A008473 = lambda n: prod(sum(pk) for pk in factorint(n).items())
isok = lambda n: A008473(n) == n
print([n for n in range(1, 10**6) if isok(n)])