A286451 Compound filter (2-adic valuation of sigma(n) & 2-adic valuation of n): a(n) = P(A286357(n), A001511(n)), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = 0 by an explicit convention.

0, 2, 6, 4, 3, 9, 10, 7, 1, 5, 6, 13, 3, 14, 10, 11, 3, 2, 6, 8, 21, 9, 10, 18, 1, 5, 10, 19, 3, 14, 21, 16, 15, 5, 15, 4, 3, 9, 10, 12, 3, 27, 6, 13, 3, 14, 15, 24, 1, 2, 10, 8, 3, 14, 10, 25, 15, 5, 6, 19, 3, 27, 10, 22, 6, 20, 6, 8, 21, 20, 10, 7, 3, 5, 6, 13, 21, 14, 15, 17, 1, 5, 6, 34, 6, 9, 10, 18, 3, 5, 15, 19, 36, 20, 10, 31, 3, 2, 6, 4, 3, 14, 10

Offset

1,2

Links

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

Eric Weisstein's World of Mathematics, Pairing Function

Formula

a(1) = 0; for n > 1, a(n) = (1/2)*(2 + ((A286357(n)+A001511(n))^2) - A286357(n) - 3*A001511(n)).

Prog

(PARI)
A001511(n) = (1+valuation(n, 2));
A286357(n) = A001511(sigma(n));
A286451(n) = if(1==n, 0, (1/2)*(2 + ((A286357(n)+A001511(n))^2) - A286357(n) - 3*A001511(n)));
for(n=1, 10000, write("b286451.txt", n, " ", A286451(n)));
(Scheme) (define (A286451 n) (if (= 1 n) 0 (* (/ 1 2) (+ (expt (+ (A286357 n) (A001511 n)) 2) (- (A286357 n)) (- (* 3 (A001511 n))) 2))))
(Python)
from sympy import divisor_sigma as D
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(a001511(D(n)), a001511(n)) # Indranil Ghosh, May 14 2017

Crossrefs

Cf. A000027, A001511, A286357, A286260, A286358.

Sequence in context: A003571 A068457 A299402 * A102510 A206225 A208507

Adjacent sequences: A286448 A286449 A286450 * A286452 A286453 A286454

Keyword

nonn

Author

Antti Karttunen, May 13 2017

Status

approved