OFFSET
1,1
COMMENTS
Or numbers having infinitary divisor 4, or the same, having factor 4 in Fermi-Dirac representation as a product of distinct terms of A050376.
From Peter Munn, Aug 25 2020: (Start)
Compare the terms, as a set, with A145204\{0} (numbers having 3 as a Fermi-Dirac factor). The self-inverse function defined by A225546 maps the members of either one of these sets 1:1 onto the other set.
Numbers whose 4th-power-free part is divisible by 4.
(End)
Numbers k such that the exponent of the highest power of 4 dividing k, A235127(k), is odd. The asymptotic density of this sequence is 1/5. - Amiram Eldar, Sep 20 2020
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 1..10000
FORMULA
Conjecture. For n>=1, a(n) = A171949(n+1).
MAPLE
isA007814 := proc(n)
if modp( A007814(n), 4) in {2, 3} then
true ;
else
false ;
end if;
end proc:
for n from 1 to 1000 do
if isA007814(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Nov 22 2023
MATHEMATICA
okQ[n_] := (cnt = Count[ Split[ IntegerDigits[n, 2]] // Last, 0]; k0 = k /. ToRules@ Reduce[ (cnt == 2*k || cnt == 2*k+1), k, Integers]; OddQ[k0]); Select[ Range[312], okQ] (* Jean-François Alcover, Mar 18 2013 *)
Select[Map[# Boole[IntegerQ[(1/4 (1+#))]||IntegerQ[(1/4 (2+#))]&[Length[Last[Split[IntegerDigits[#, 2]]]]]]&, Range[2, 500, 2]], #>0&]
Select[Range[280], OddQ @ IntegerExponent[#, 4] &] (* Amiram Eldar, Sep 20 2020 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Mar 18 2013
EXTENSIONS
Named edited by David A. Corneth, Sep 22 2020
STATUS
approved