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A170819 a(n) = product of distinct primes of the form 4k-1 that divide n.

%I A170819 #23 Jul 06 2023 08:55:11
%S A170819 1,1,3,1,1,3,7,1,3,1,11,3,1,7,3,1,1,3,19,1,21,11,23,3,1,1,3,7,1,3,31,
%T A170819 1,33,1,7,3,1,19,3,1,1,21,43,11,3,23,47,3,7,1,3,1,1,3,11,7,57,1,59,3,
%U A170819 1,31,21,1,1,33,67,1,69,7,71,3,1,1,3,19,77,3,79,1,3,1,83,21,1
%N A170819 a(n) = product of distinct primes of the form 4k-1 that divide n.
%H A170819 Michael De Vlieger, <a href="/A170819/b170819.txt">Table of n, a(n) for n = 1..10000</a>
%F A170819 Multiplicative with a(p^e) = p^A011765(p+1), e > 0. - _R. J. Mathar_, Jun 07 2011
%F A170819 a(n) = A007947(A097706(n)) = A097706(A007947(n)). - _Peter Munn_, Jul 06 2023
%p A170819 A170819 := proc(n) a := 1 ; for p in numtheory[factorset](n) do if p mod 4 = 3 then a := a*p ; end if; end do: a ; end proc:
%p A170819 seq(A170819(n),n=1..20) ; # _R. J. Mathar_, Jun 07 2011
%t A170819 Array[Times @@ Select[FactorInteger[#][[All, 1]], Mod[#, 4] == 3 &] &, 85] (* _Michael De Vlieger_, Feb 19 2019 *)
%o A170819 (PARI) for(n=1,99, t=select(x->x%4==3, factor(n)[,1]); print1(prod(i=1,#t,t[i])","))
%Y A170819 Cf. A007947, A011765, A065339, A097706, A170817, A170818, A363340.
%K A170819 nonn,mult
%O A170819 1,3
%A A170819 _N. J. A. Sloane_, Dec 23 2009
%E A170819 Extended with PARI program by _M. F. Hasler_, Dec 23 2009