A319522 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).

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

Offset: 1

Author

Rémy Sigrist, Sep 22 2018

Keywords

• nonn
• mult

Comments

See A319521 for a similar sequence and additional comments.

Examples

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

Crossrefs

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

Programs

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))

Formula

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

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

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

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