cp's OEIS Frontend

A202237 Odd numbers with the same number of prime factors of the form 4*k+1 and 4*k+3.

%I A202237 #21 Jun 15 2025 09:14:15
%S A202237 1,15,35,39,51,55,87,91,95,111,115,119,123,143,155,159,183,187,203,
%T A202237 215,219,225,235,247,259,267,287,291,295,299,303,319,323,327,335,339,
%U A202237 355,371,391,395,403,407,411,415,427,447,451,471,511,515,519,525,527,535,543,551
%N A202237 Odd numbers with the same number of prime factors of the form 4*k+1 and 4*k+3.
%C A202237 Primes are counted with multiplicity.
%C A202237 Closed under multiplication.
%H A202237 Amiram Eldar, <a href="/A202237/b202237.txt">Table of n, a(n) for n = 1..10000</a>
%p A202237 isA202237 := proc(n)
%p A202237     if type(n,'odd') then
%p A202237         A083025(n) = A065339(n) ;
%p A202237     else
%p A202237         false;
%p A202237     end if;
%p A202237 end proc:
%p A202237 for n from 1 to 200 do
%p A202237     if isA202237(n) then
%p A202237         printf("%d,",n);
%p A202237     end if;
%p A202237 end do: # _R. J. Mathar_, Dec 16 2011
%t A202237 fQ[n_]:=Plus@@((Mod[#[[1]], 4]-2)*#[[2]]&/@If[n==1, {}, FactorInteger[n]])==0 && OddQ[n]; Select[Range[600], fQ] (* _Ray Chandler_, Dec 20 2011 *)
%o A202237 (PARI) netprime(n)=local(fm=factor(n));sum(k=1,matsize(fm)[1],if(fm[k,1]==2,0,if(fm[k,1]%4==1,fm[k,2],-fm[k,2])))
%o A202237 ap(n)=forstep(k=1,n,2,if(netprime(k)==0,print1(k", ")))
%Y A202237 Cf. A080774 (primitive elements), A072202 (even allowed).
%K A202237 nonn
%O A202237 1,2
%A A202237 _Franklin T. Adams-Watters_, Dec 16 2011