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A286259
Compound filter: a(n) = P(A001511(n), A049820(n)), where P(n,k) is sequence A000027 used as a pairing function.
2
1, 2, 1, 6, 4, 5, 11, 25, 16, 23, 37, 31, 56, 57, 56, 110, 106, 80, 137, 123, 137, 173, 211, 175, 232, 255, 254, 279, 352, 255, 407, 471, 407, 467, 466, 409, 596, 597, 596, 599, 742, 597, 821, 783, 742, 905, 991, 866, 1036, 992, 1082, 1131, 1276, 1083, 1276, 1279, 1379, 1487, 1597, 1228, 1712, 1713, 1597, 1960, 1831, 1713, 2081, 2019, 2081, 1955, 2347, 1957
OFFSET
1,2
LINKS
FORMULA
a(n) = (1/2)*(2 + ((A001511(n)+A049820(n))^2) - A001511(n) - 3*A049820(n)).
PROG
(PARI)
A001511(n) = (1+valuation(n, 2));
A049820(n) = (n-numdiv(n));
A286259(n) = (2 + ((A001511(n)+A049820(n))^2) - A001511(n) - 3*A049820(n))/2;
for(n=1, 10000, write("b286259.txt", n, " ", A286259(n)));
(Scheme) (define (A286259 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A049820 n)) 2) (- (A001511 n)) (- (* 3 (A049820 n))) 2)))
(Python)
from sympy import divisor_count as d
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")
def a(n): return T(a001511(n), n - d(n)) # Indranil Ghosh, May 07 2017
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 07 2017
STATUS
approved