login
A329575
Numbers whose smallest Fermi-Dirac factor is 3.
7
3, 12, 15, 21, 27, 33, 39, 48, 51, 57, 60, 69, 75, 84, 87, 93, 105, 108, 111, 123, 129, 132, 135, 141, 147, 156, 159, 165, 177, 183, 189, 192, 195, 201, 204, 213, 219, 228, 231, 237, 240, 243, 249, 255, 267, 273, 276, 285, 291, 297, 300, 303, 309, 321, 327, 336, 339, 345
OFFSET
1,1
COMMENTS
Every positive integer is the product of a unique subset of the terms of A050376 (sometimes called Fermi-Dirac primes). This sequence lists the numbers where the relevant subset includes 3 but not 2.
Numbers whose squarefree part is divisible by 3 but not 2.
Positive multiples of 3 that survive sieving by the rule: if m appears then 2m, 3m and 6m do not. Asymptotic density is 1/6.
LINKS
FORMULA
A223490(a(n)) = 3.
A007913(a(n)) == 3 (mod 6).
A059897(2, a(n)) = 2 * a(n).
A059897(3, a(n)) * 3 = a(n).
{a(n) : n >= 1} = {k : 3 * A307150(k) = 2 * k}.
A003159 = {a(n) / 3 : n >= 1} U {a(n) : n >= 1}.
A036668 = {a(n) / 3 : n >= 1} U {a(n) * 2 : n >= 1}.
A145204 \ {0} = {a(n) : n >= 1} U {a(n) * 2 : n >= 1}.
EXAMPLE
6 is the product of the following terms of A050376: 2, 3. These terms include 2, so 6 is not in the sequence.
12 is the product of the following terms of A050376: 3, 4. These terms include 3, but not 2, so 12 is in the sequence.
20 is the product of the following terms of A050376: 4, 5. These terms do not include 3, so 20 is not in the sequence.
MATHEMATICA
f[p_, e_] := p^(2^IntegerExponent[e, 2]); fdmin[n_] := Min @@ f @@@ FactorInteger[n]; Select[Range[350], fdmin[#] == 3 &] (* Amiram Eldar, Nov 27 2020 *)
PROG
(PARI) isok(m) = core(m) % 6 == 3; \\ Michel Marcus, May 01 2020
CROSSREFS
Intersection of any 2 of A003159, A145204 and A325424; also subsequence of A028983.
Ordered 3rd quadrisection of A052330.
Sequence in context: A044828 A248105 A269315 * A022380 A331074 A290593
KEYWORD
nonn
AUTHOR
Peter Munn, Apr 27 2020
STATUS
approved