A292584 Compound filter: a(n) = P(A292583(n), A292585(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 2, 5, 2, 8, 5, 13, 2, 4, 8, 19, 5, 25, 13, 9, 2, 32, 4, 41, 8, 12, 19, 51, 5, 16, 25, 5, 13, 72, 9, 85, 2, 18, 32, 14, 4, 98, 41, 26, 8, 112, 12, 128, 19, 8, 51, 145, 5, 46, 16, 33, 25, 180, 5, 18, 13, 49, 72, 200, 9, 220, 85, 13, 2, 24, 18, 242, 32, 60, 14, 265, 4, 288, 98, 8, 41, 19, 26, 313, 8, 4, 112, 339, 12, 33, 128, 62, 19, 365, 8, 25, 51, 84, 145

Offset

1,2

Comments

From Antti Karttunen, Sep 25 2017: (Start)

Some of the sequences this filter matches to:

For all i, j: a(i) = a(j) => A053866(i) = A053866(j).

For all i, j: a(i) = a(j) => A061395(i) = A061395(j). (also A006530, etc.)

For all i, j: a(i) = a(j) => A292378(i) = A292378(j).

The latter two implications follow simply because:

A001222(A278222(A292383(n))) = A000120(A292383(n)) = A292377(n)

and, similarly, for n > 1,

A001222(A278222(A292385(n))) = A000120(A292381(n)) = A292375(n),

and the sum of A292375(n) and A292377(n) is A061395(n) [index of the largest prime dividing n], while A292378 has been defined as 1 + their difference.

The case A053866 follows because of the component A292583, see comments under that entry. (End)

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = (1/2)*(2 + ((A292583(n)+A292585(n))^2) - A292583(n) - 3*A292585(n)).

Crossrefs

Cf. A292383, A292385, A292583, A292585.

Cf. also A006530, A061395, A292378 (some of the matched sequences).

Sequence in context: A065223 A248154 A274415 * A029621 A240223 A134349

Adjacent sequences: A292581 A292582 A292583 * A292585 A292586 A292587

Keyword

nonn

Author

Antti Karttunen, Sep 20 2017

Status

approved