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

1, 15, 35, 39, 51, 55, 87, 91, 95, 111, 115, 119, 123, 143, 155, 159, 183, 187, 203, 215, 219, 225, 235, 247, 259, 267, 287, 291, 295, 299, 303, 319, 323, 327, 335, 339, 355, 371, 391, 395, 403, 407, 411, 415, 427, 447, 451, 471, 511, 515, 519, 525, 527, 535, 543, 551

Offset: 1

Author

Franklin T. Adams-Watters, Dec 16 2011

Keywords

• nonn

Comments

Primes are counted with multiplicity.

Closed under multiplication.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A080774 (primitive elements), A072202 (even allowed).

Programs

Maple

isA202237 := proc(n)
    if type(n,'odd') then
        A083025(n) = A065339(n) ;
    else
        false;
    end if;
end proc:
for n from 1 to 200 do
    if isA202237(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Dec 16 2011

Mathematica

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 *)

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])))
ap(n)=forstep(k=1,n,2,if(netprime(k)==0,print1(k", ")))