cp's OEIS Frontend

A072010 In prime factorization of n replace all primes of form k*4+1 with k*4+3 and primes of form k*4+3 with k*4+1.

%I A072010 #18 Mar 31 2017 21:58:14
%S A072010 1,2,1,4,7,2,5,8,1,14,9,4,15,10,7,16,19,2,17,28,5,18,21,8,49,30,1,20,
%T A072010 31,14,29,32,9,38,35,4,39,34,15,56,43,10,41,36,7,42,45,16,25,98,19,60,
%U A072010 55,2,63,40,17,62,57,28,63,58,5,64,105,18,65,76,21,70,69
%N A072010 In prime factorization of n replace all primes of form k*4+1 with k*4+3 and primes of form k*4+3 with k*4+1.
%C A072010 a(3^n) = 1; a(2^n) = 2^n;
%C A072010 a(n)>2 is prime iff n=m*3^i (i>=0), a(n)=a(m) and (m,a(m)) or (a(m),m) is a twin prime pair of form ((4*k+1),(4*k+3)), a(m)*m=A071697(j)=A071695(j)*A071696(j) for some j.
%H A072010 T. D. Noe, <a href="/A072010/b072010.txt">Table of n, a(n) for n=1..1000</a>
%F A072010 Multiplicative with a(p) = p + 2*(2 - p mod 4), p prime.
%e A072010 a(26928) = a(2^4*3^2*11*17) = a(2)^4 * a(3)^2 * a(11) * a(17)
%e A072010 = 2^4 * 1^2 * 9 * 19 = 2736.
%t A072010 a[1] = 1; a[p_?PrimeQ] = p + 2*(2 - Mod[p, 4]); a[n_] := Times @@ (a[#[[1]]]^#[[2]] & ) /@ FactorInteger[n]; Table[a[n], {n, 1, 71}] (* _Jean-François Alcover_, May 04 2012 *)
%o A072010 (Haskell)
%o A072010 a072010 1 = 1
%o A072010 a072010 n = product $ map f $ a027746_row n where
%o A072010    f 2 = 2
%o A072010    f p = p + 2 * (2 - p `mod` 4)
%o A072010 -- _Reinhard Zumkeller_, Apr 09 2012
%Y A072010 Cf. A002144, A002145, A072012(n) = a(a(n)).
%Y A072010 For a(n) = n see A072011.
%Y A072010 Cf. A072014, A072015.
%Y A072010 Cf. A027746.
%K A072010 nonn,mult,nice
%O A072010 1,2
%A A072010 _Reinhard Zumkeller_, Jun 05 2002