OFFSET
1,2
COMMENTS
Or, numbers that are not divisible by the sum of two squares (other than 1). - Clarified by Gabriel Conant, Apr 18 2016
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Rafael Jakimczuk, Generalizations of Mertens's Formula and k-Free and s-Full Numbers with Prime Divisors in Arithmetic Progression, ResearchGate, 2024.
FORMULA
The number of terms that do not exceed x is ~ c * x / sqrt(log(x)), where c = A243379/(2*sqrt(A175647)) = 0.4165140462... (Jakimczuk, 2024, Theorem 3.10, p. 26). - Amiram Eldar, Mar 08 2024
MAPLE
N:= 1000: # to get all terms <= N
S:= {1};
for p from 3 by 4 to N do
if isprime(p) then
S:= S union select(`<=`, map(t -> t*p, S), N)
fi
od:
sort(convert(S, list)); # Robert Israel, Apr 18 2016
MATHEMATICA
Select[Range@ 1000, #==1 || ({{3}, {1}} == Union /@ {Mod[ #[[1]], 4], #[[2]]} &@ Transpose@ FactorInteger@ #) &] (* Giovanni Resta, Apr 18 2016 *)
PROG
(PARI) isok(n) = if (! issquarefree(n), return (0)); f = factor(n); for (i=1, #f~, if (f[i, 1] % 4 != 3, return (0))); 1 \\ Michel Marcus, Sep 04 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Arnaud Vernier, Oct 29 2009
EXTENSIONS
Edited by Zak Seidov, Oct 30 2009
Narrowed definition down to squarefree numbers - R. J. Mathar, Nov 05 2009
STATUS
approved