A286456 -id:A286456 - cp's OEIS frontend

A286454 Compound filter (prime signature & prime signature of conjugated prime factorization): a(n) = P(A101296(n), A286621(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 5, 8, 9, 12, 32, 23, 20, 13, 49, 38, 51, 47, 82, 49, 35, 68, 51, 80, 72, 124, 140, 122, 74, 18, 175, 26, 111, 155, 334, 192, 65, 257, 280, 82, 116, 255, 329, 355, 99, 327, 570, 380, 177, 72, 469, 437, 132, 31, 72, 532, 216, 498, 74, 257, 144, 599, 634, 597, 448, 632, 745, 159, 119, 784, 1044, 782, 331, 907, 570, 863, 186, 905, 1039, 72, 384, 140, 1335, 1037

Offset: 1

Antti Karttunen, May 14 2017

nonn

Here, instead of A046523 and A278221 we use as the components of a(n) their rgs-versions A101296 and A286621 because of the latter sequence's moderate growth rates.

For all i, j: a(i) = a(j) => A286356(i) = A286356(j).

Antti Karttunen, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pairing Function

Cf. A000027, A046523, A101296, A122111, A278221, A285334, A286621, A286356, A286455, A286456.

(define (A286454 n) (* (/ 1 2) (+ (expt (+ (A101296 n) (A286621 n)) 2) (- (A101296 n)) (- (* 3 (A286621 n))) 2)))

a(n) = (1/2)*(2 + ((A101296(n)+A286621(n))^2) - A101296(n) - 3*A286621(n)).

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.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, May 14 2017

nonn

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).

Antti Karttunen, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pairing Function

Cf. A000027, A055396, A122111, A243055, A278221, A285334, A286621, A286454, A286456.

(define (A286455 n) (* (/ 1 2) (+ (expt (+ (A055396 n) (A286621 n)) 2) (- (A055396 n)) (- (* 3 (A286621 n))) 2)))

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

cp's OEIS Frontend

A286454 Compound filter (prime signature & prime signature of conjugated prime factorization): a(n) = P(A101296(n), A286621(n)), where P(n,k) is sequence A000027 used as a pairing function.

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