A286592 Compound filter (prime signature & deficiency/abundance): a(n) = P(A046523(n), A286449(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 3, 5, 10, 8, 42, 17, 36, 40, 27, 30, 183, 47, 34, 51, 136, 57, 243, 80, 288, 72, 177, 122, 765, 194, 72, 308, 117, 192, 1020, 212, 528, 142, 259, 196, 1576, 255, 111, 196, 1059, 302, 1020, 327, 103, 202, 471, 380, 2823, 500, 832, 306, 132, 498, 765, 672, 1564, 747, 786, 668, 4620, 743, 282, 337, 2080, 502, 1020, 782, 165, 441, 696, 822, 6288, 905, 747, 1047, 202

Offset: 1

Author

Antti Karttunen, May 21 2017

Keywords

• nonn

Comments

The lowermost conspicuous horizontal line in the scatter plot (at about log 3) is caused by value 1020, which corresponds to the prime signature 30 (p*q*r) and deficiency -12 packed together with the pairing function (as A002260(1020) = 30 and A004736(1020) = 16, A286449(24) = 16 and A033879(24) = -12). This value occurs in this sequence (at least) in the positions given by A138636, from its third term 30 onward.

Links

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

Crossrefs

Cf. A000027, A033879, A033880, A046523, A138636, A286449, A286593, A286595.

Programs

Scheme

(define (A286592 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A286449 n)) 2) (- (A046523 n)) (- (* 3 (A286449 n))) 2)))

Formula

a(n) = (1/2)*(2 + ((A046523(n)+A286449(n))^2) - A046523(n) - 3*A286449(n)).