cp's OEIS Frontend

A348746 Fully multiplicative with a(2) = 3, a(3) = 5, a(A002144(n)) = A002144(1+n) and a(A002145(1+n)) = a(A002145(1+n)) for all n >= 1, where A002144 and A002145 give the primes of the form 4k+1 and 4k+3 respectively.

%I A348746 #13 Apr 25 2022 14:02:09
%S A348746 1,3,5,9,13,15,7,27,25,39,11,45,17,21,65,81,29,75,19,117,35,33,23,135,
%T A348746 169,51,125,63,37,195,31,243,55,87,91,225,41,57,85,351,53,105,43,99,
%U A348746 325,69,47,405,49,507,145,153,61,375,143,189,95,111,59,585,73,93,175,729,221,165,67,261,115,273,71,675,89,123
%N A348746 Fully multiplicative with a(2) = 3, a(3) = 5, a(A002144(n)) = A002144(1+n) and a(A002145(1+n)) = a(A002145(1+n)) for all n >= 1, where A002144 and A002145 give the primes of the form 4k+1 and 4k+3 respectively.
%C A348746 Permutation of odd numbers. Preserves the prime signature.
%H A348746 Antti Karttunen, <a href="/A348746/b348746.txt">Table of n, a(n) for n = 1..10000</a>
%F A348746 Fully multiplicative with a(p) = A348744(A000720(p)), where A348744 is the lexicographically earliest bijection from primes to odd primes where each prime of the form 4k+1 is mapped to the next larger prime of the same form.
%o A348746 (PARI) A348746(n) = { my(f=factor(n)); for(k=1,#f~, if(2==f[k,1], f[k,1]=3, if(3==f[k,1], f[k,1]=5, if(1==(f[k,1]%4), for(i=1+primepi(f[k,1]),oo,if(1==(prime(i)%4), f[k,1]=prime(i); break)))))); factorback(f); };
%Y A348746 Cf. A000720, A002144, A002145, A348744, A348747 (left inverse).
%Y A348746 Cf. also A003961, A332818 for similar maps.
%K A348746 nonn,mult
%O A348746 1,2
%A A348746 _Antti Karttunen_, Nov 02 2021