A223491 Largest Fermi-Dirac factor of n.

1, 2, 3, 4, 5, 3, 7, 4, 9, 5, 11, 4, 13, 7, 5, 16, 17, 9, 19, 5, 7, 11, 23, 4, 25, 13, 9, 7, 29, 5, 31, 16, 11, 17, 7, 9, 37, 19, 13, 5, 41, 7, 43, 11, 9, 23, 47, 16, 49, 25, 17, 13, 53, 9, 11, 7, 19, 29, 59, 5, 61, 31, 9, 16, 13, 11, 67, 17, 23, 7, 71, 9

Offset

1,2

Comments

Greatest Fermi-Dirac factor of n: Largest divisor of n of the form p^(2^k), for some prime p and k >= 0, with a(1) = 1. Thus for n > 1, the largest term of A050376 that divides n. - Antti Karttunen, Apr 13 2018

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

OEIS Wiki, "Fermi-Dirac representation" of n

Formula

a(n) = A213925(n,A064547(n)).

A209229(A100995(a(n))) = 1; A010055(a(n)) = 1.

From Antti Karttunen, Apr 13 2018: (Start)

a(1) = 1; for n > 1, a(n) = A050376(A302785(n)).

a(n) = n/A302776(n).

(End)

Mathematica

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

Prog

(Haskell)
a223491 = last . a213925_row
(PARI)
ispow2(n) = (n && !bitand(n, n-1));
A223491(n) = if(1==n, n, fordiv(n, d, if(ispow2(isprimepower(n/d)), return(n/d)))); \\ Antti Karttunen, Apr 13 2018

Crossrefs

Cf. A223490, A050376, A034699, A000040 (subsequence), A302776, A302785, A302789 (ordinal transform).

Cf. also A006530, A034699.

Sequence in context: A088491 A353172 A140271 * A346088 A275823 A141295

Adjacent sequences: A223488 A223489 A223490 * A223492 A223493 A223494

Keyword

nonn

Author

Reinhard Zumkeller, Mar 20 2013

Status

approved