A223490 Smallest Fermi-Dirac factor of n.

1, 2, 3, 4, 5, 2, 7, 2, 9, 2, 11, 3, 13, 2, 3, 16, 17, 2, 19, 4, 3, 2, 23, 2, 25, 2, 3, 4, 29, 2, 31, 2, 3, 2, 5, 4, 37, 2, 3, 2, 41, 2, 43, 4, 5, 2, 47, 3, 49, 2, 3, 4, 53, 2, 5, 2, 3, 2, 59, 3, 61, 2, 7, 4, 5, 2, 67, 4, 3, 2, 71, 2, 73, 2, 3, 4, 7, 2, 79

Offset

1,2

Comments

Note that this is not equal to the smallest Fermi-Dirac prime (A050376) dividing n, which is always A020639(n). - Antti Karttunen, Apr 15 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,1).

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

From Antti Karttunen, Apr 15 2018: (Start)

a(1) = 1; and for n > 1, a(n) = A050376(A302786(n)).

a(n) = n / A302792(n).

a(n) = A302023(A020639(A302024(n))).

(End)

Mathematica

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

Prog

(Haskell)
a223490 = head . a213925_row
(PARI)
up_to = 65537;
v050376 = vector(up_to);
A050376(n) = v050376[n];
ispow2(n) = (n && !bitand(n, n-1));
i = 0; for(n=1, oo, if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to, break));
A052331(n) = { my(s=0, e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
A001511(n) = 1+valuation(n, 2);
A223490(n) = if(1==n, n, A050376(A001511(A052331(n)))); \\ Antti Karttunen, Apr 15 2018

Crossrefs

Cf. A223491, A050376, A028233, A000040 (subsequence).

Cf. A302023, A302024, A302786, A302792.

Cf. also A020639.

Sequence in context: A353277 A308201 A026362 * A354749 A244734 A230089

Adjacent sequences: A223487 A223488 A223489 * A223491 A223492 A223493

Keyword

nonn,look

Author

Reinhard Zumkeller, Mar 20 2013

Status

approved