A286455 - OEIS

A286455

Compound filter (smallest prime dividing n & prime signature of conjugated prime factorization): a(n) = P(A055396(n), A286621(n)), where P(n,k) is sequence A000027 used as a pairing function.

0, 2, 8, 2, 18, 11, 40, 2, 8, 22, 71, 11, 97, 46, 30, 2, 143, 11, 179, 22, 93, 92, 262, 11, 18, 121, 8, 46, 335, 154, 417, 2, 212, 211, 69, 11, 540, 254, 302, 22, 679, 326, 794, 92, 30, 379, 918, 11, 40, 22, 467, 121, 1051, 11, 234, 46, 530, 529, 1242, 154, 1344, 631, 93, 2, 744, 704, 1615, 211, 822, 326, 1790, 11, 1912, 904, 30, 254, 140, 947, 2167, 22, 8

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OFFSET

1,2

COMMENTS

Note that as the other component of a(n) we use A286621 instead of A278221, because of latter sequence's unwieldy large terms.

For all i, j: a(i) = a(j) => A243055(i) = A243055(j).

For all i, j: a(i) = a(j) => A286470(i) = A286470(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Pairing Function

FORMULA

a(n) = (1/2)*(2 + ((A055396(n)+A286621(n))^2) - A055396(n) - 3*A286621(n)).