A319522 - OEIS

%I #10 Aug 11 2022 09:57:42

%S 1,1,2,1,1,2,3,1,4,1,1,2,5,3,2,1,1,4,7,1,6,1,1,2,1,5,8,3,11,2,1,1,2,1,

%T 3,4,13,7,10,1,1,6,17,1,4,1,1,2,9,1,2,5,19,8,1,3,14,11,1,2,23,1,12,1,

%U 5,2,1,1,2,3,29,4,1,13,2,7,3,10,31,1,16,1

%N Completely multiplicative with a(prime(2*k)) = prime(k) and a(prime(2*k-1)) = 1 for any k > 0 (where prime(k) denotes the k-th prime number).

%C See A319521 for a similar sequence and additional comments.

%F a(n) = 1 iff n belongs to A066208.

%F a(n) <= n with equality iff n = 1.

%F A007814(a(n)) = A007949(n).

%F a(n) = A319521(A064989(n)).

%e a(42) = a(prime(1)) * a(prime(2)) * a(prime(4)) = 1 * prime(1) * prime(2) = 6.

%o (PARI) a(n) = my (f=factor(n)); prod(i=1, #f~, my (pi=primepi(f[i,1])); if (pi%2==0, prime(pi/2)^f[i,2], 1))

%Y Cf. A007814, A007949, A064989, A066208, A319521.

%K nonn,mult

%O 1,3

%A _Rémy Sigrist_, Sep 22 2018