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A292584
Compound filter: a(n) = P(A292583(n), A292585(n)), where P(n,k) is sequence A000027 used as a pairing function.
6
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:
and, similarly, for n > 1,
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)
FORMULA
a(n) = (1/2)*(2 + ((A292583(n)+A292585(n))^2) - A292583(n) - 3*A292585(n)).
CROSSREFS
Cf. also A006530, A061395, A292378 (some of the matched sequences).
Sequence in context: A065223 A248154 A274415 * A029621 A240223 A134349
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 20 2017
STATUS
approved