cp's OEIS Frontend

A348747 Fully multiplicative with a(2) = 1, a(3) = 2, a(5) = 3, a(A002144(1+n)) = A002144(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 A348747 #13 Nov 02 2021 20:59:47
%S A348747 1,1,2,1,3,2,7,1,4,3,11,2,5,7,6,1,13,4,19,3,14,11,23,2,9,5,8,7,17,6,
%T A348747 31,1,22,13,21,4,29,19,10,3,37,14,43,11,12,23,47,2,49,9,26,5,41,8,33,
%U A348747 7,38,17,59,6,53,31,28,1,15,22,67,13,46,21,71,4,61,29,18,19,77,10,79,3,16,37,83,14,39,43,34,11,73
%N A348747 Fully multiplicative with a(2) = 1, a(3) = 2, a(5) = 3, a(A002144(1+n)) = A002144(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.
%F A348747 Fully multiplicative with a(p) = A348745(A000720(p)).
%F A348747 a(A348746(n)) = n.
%F A348747 a(2n) = a(A000265(n)) = a(n).
%o A348747 (PARI) A348747(n) = { my(f=factor(n)); for(k=1,#f~, if(f[k,1]<=3, f[k,1]--, if(5==f[k,1], f[k,1]=3, if(1==(f[k,1]%4), forstep(i=primepi(f[k,1])-1,0,-1,if(1==(prime(i)%4), f[k,1]=prime(i); break)))))); factorback(f); };
%Y A348747 Left inverse of A348746.
%Y A348747 Cf. A000265, A000720, A002144, A002145, A348745.
%Y A348747 Cf. also A064989, A332819 for similar maps.
%K A348747 nonn,mult
%O A348747 1,3
%A A348747 _Antti Karttunen_, Nov 02 2021