A286388 Compound filter ("discard the smallest prime factor" & "number of trailing 1-bits in base-2"): a(n) = P(A032742(n), A001511(1+n)), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = 0.

0, 1, 4, 3, 2, 6, 7, 10, 9, 15, 4, 21, 2, 28, 41, 36, 2, 45, 4, 55, 35, 66, 7, 78, 20, 91, 64, 105, 2, 120, 16, 136, 77, 153, 43, 171, 2, 190, 133, 210, 2, 231, 4, 253, 135, 276, 11, 300, 35, 325, 188, 351, 2, 378, 102, 406, 209, 435, 4, 465, 2, 496, 372, 528, 104, 561, 4, 595, 299, 630, 7, 666, 2, 703, 376, 741, 77, 780, 11, 820, 405, 861, 4, 903, 170, 946

Offset: 1

Author

Antti Karttunen, May 13 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000027, A001511, A032742, A286379, A286386.

Programs

Python

from sympy import divisors
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a001511(n): return bin(n)[2:][::-1].index("1") + 1
def a(n): return 0 if n==1 else T(divisors(n)[-2], a001511(n + 1)) # Indranil Ghosh, May 14 2017

Scheme

(define (A286388 n) (if (= 1 n) 0 (* (/ 1 2) (+ (expt (+ (A032742 n) (A001511 (+ 1 n))) 2) (- (A032742 n)) (- (* 3 (A001511 (+ 1 n)))) 2))))

Formula

a(1) = 0, for n > 1, a(n) = (1/2)*(2 + ((A032742(n)+A001511(1+n))^2) - A032742(n) - 3*A001511(1+n)).