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

1,2

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

Formula

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

Prog

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

Crossrefs

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

Sequence in context: A365440 A332359 A328070 * A176629 A069193 A078430

Adjacent sequences: A286589 A286590 A286591 * A286593 A286594 A286595

Keyword

nonn

Author

Antti Karttunen, May 21 2017

Status

approved