A286260 Compound filter: a(n) = P(A001511(n), A161942(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 8, 1, 39, 4, 8, 1, 157, 79, 47, 4, 39, 22, 8, 4, 600, 37, 782, 11, 256, 1, 47, 4, 157, 466, 233, 11, 39, 106, 47, 1, 2284, 4, 380, 4, 4281, 172, 122, 22, 1132, 211, 8, 56, 256, 742, 47, 4, 600, 1597, 4373, 37, 1278, 352, 122, 37, 157, 11, 1037, 106, 256, 466, 8, 79, 8785, 211, 47, 137, 2083, 4, 47, 37, 19507, 667, 1655, 466, 669, 4, 233, 11, 4661, 7261

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

MathWorld, Pairing Function

Formula

a(n) = (1/2)*(2 + ((A001511(n)+A161942(n))^2) - A001511(n) - 3*A161942(n)).

Prog

(PARI)
A001511(n) = (1+valuation(n, 2));
A000265(n) = (n >> valuation(n, 2));
A161942(n) = A000265(sigma(n));
A286260(n) = (2 + ((A001511(n)+A161942(n))^2) - A001511(n) - 3*A161942(n))/2;
for(n=1, 16384, write("b286260.txt", n, " ", A286260(n)));
(Scheme) (define (A286260 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A161942 n)) 2) (- (A001511 n)) (- (* 3 (A161942 n))) 2)))
(Python)
from sympy import factorint, divisors, divisor_sigma
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a000265(n): return max(list(filter(lambda i: i%2 == 1, divisors(n))))
def a161942(n): return a000265(divisor_sigma(n))
def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")
def a(n): return T(a001511(n), a161942(n)) # Indranil Ghosh, May 07 2017

Crossrefs

Cf. A000027, A001511, A161942, A286161, A286162, A286259, A286034.

Sequence in context: A050302 A341739 A286919 * A226374 A050401 A333403

Adjacent sequences: A286257 A286258 A286259 * A286261 A286262 A286263

Keyword

nonn

Author

Antti Karttunen, May 07 2017

Status

approved