login
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.
4
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
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)))
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 21 2017
STATUS
approved