This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A319521 #11 Sep 24 2018 08:55:18 %S A319521 1,2,1,4,3,2,1,8,1,6,5,4,1,2,3,16,7,2,1,12,1,10,11,8,9,2,1,4,1,6,13, %T A319521 32,5,14,3,4,1,2,1,24,17,2,1,20,3,22,19,16,1,18,7,4,1,2,15,8,1,2,23, %U A319521 12,1,26,1,64,3,10,29,28,11,6,1,8,31,2,9,4,5,2,1 %N A319521 Completely multiplicative with a(prime(2*k-1)) = prime(k) and a(prime(2*k)) = 1 for any k > 0 (where prime(k) denotes the k-th prime number). %C A319521 See A319522 for a similar sequence. %C A319521 The function n -> (a(n), A319522(n)) establishes a bijection from N to N x N (where N = A000027); see A319523 for the corresponding inverse function. %C A319521 This sequence has similarities with A059905: here we keep one p-adic valuation out of two, there we keep one binary digit out of two. %F A319521 a(n) = 1 iff n = 1 or n belongs to A066207. %F A319521 a(n) <= n with equality iff n is a power of 2 (A000079). %F A319521 A007814(a(n)) = A007814(n). %e A319521 a(42) = a(prime(1)) * a(prime(2)) * a(prime(4)) = prime(1) * 1 * 1 = 2. %o A319521 (PARI) a(n) = my (f=factor(n)); prod(i=1, #f~, my (pi=primepi(f[i,1])); if (pi%2==1, prime(1+pi\2)^f[i,2], 1)) %Y A319521 Cf. A000027, A000079, A007814, A059905, A066207, A319522, A319523. %K A319521 nonn,mult %O A319521 1,2 %A A319521 _Rémy Sigrist_, Sep 22 2018