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

1,3

Comments

See A319521 for a similar sequence and additional comments.

Links

Table of n, a(n) for n=1..82.

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)).

Example

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

Prog

(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))

Crossrefs

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

Sequence in context: A133771 A352895 A288158 * A366344 A379003 A217612

Adjacent sequences: A319519 A319520 A319521 * A319523 A319524 A319525

Keyword

nonn,mult

Author

Rémy Sigrist, Sep 22 2018

Status

approved