A376299 Fixed points of A008473.

1, 4, 90, 120

Offset

1,2

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

Table of n, a(n) for n=1..4.

Lucas A. Brown, Python program.

Combo Class, The Mysterious Pattern I Found Within Prime Factorizations, Sep 12 2024.

Prog

(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)])

Crossrefs

Cf. A008473, A299352.

Sequence in context: A220341 A184955 A205295 * A292304 A337081 A218385

Adjacent sequences: A376296 A376297 A376298 * A376300 A376301 A376302

Keyword

nonn,more,hard

Author

Darío Clavijo, Sep 19 2024

Status

approved