A302776 a(1) = 1; for n>1, a(n) = n/(largest Fermi-Dirac factor of n).

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 3, 1, 1, 2, 1, 4, 3, 2, 1, 6, 1, 2, 3, 4, 1, 6, 1, 2, 3, 2, 5, 4, 1, 2, 3, 8, 1, 6, 1, 4, 5, 2, 1, 3, 1, 2, 3, 4, 1, 6, 5, 8, 3, 2, 1, 12, 1, 2, 7, 4, 5, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 6, 1, 5, 1, 2, 1, 12, 5, 2, 3, 8, 1, 10, 7, 4, 3, 2, 5, 6, 1, 2, 9, 4, 1, 6, 1, 8, 15

Offset: 1

Author

Antti Karttunen, Apr 13 2018

Keywords

• nonn

Comments

For n > 1, a(n) = the smallest positive number d such that n/d is a "Fermi-Dirac prime", a term of A050376.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A050376, A052331, A223491, A302023, A302024, A302777, A302792.

Cf. A084400 (gives the positions of 1's).

Cf. also A052126, A284600.

Programs

Mathematica

f[p_, e_] := p^(2^Floor[Log2[e]]); a[n_] := n / Max @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 26 2020 *)

PARI

A209229(n) = (n && !bitand(n,n-1));
A302777(n) = A209229(isprimepower(n));
A302776(n) = if(1==n,n,fordiv(n, d, if(A302777(n/d), return(d))));

Formula

a(n) = n / A223491(n).

a(n) = A302023(A052126(A302024(n))).