A286460 Compound filter (2-adic valuation & sum of the divisors): a(n) = P(A001511(n), A000203(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 8, 7, 39, 16, 80, 29, 157, 79, 173, 67, 438, 92, 302, 277, 600, 154, 782, 191, 949, 497, 668, 277, 1957, 466, 905, 781, 1656, 436, 2630, 497, 2284, 1129, 1487, 1129, 4281, 704, 1832, 1541, 4282, 862, 4658, 947, 3658, 3004, 2630, 1129, 8133, 1597, 4373, 2557, 4953, 1432, 7262, 2557, 7507, 3161, 4097, 1771, 14368, 1892, 4658, 5357, 8785, 3487, 10442, 2279

Offset

1,2

Links

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

Eric Weisstein's World of Mathematics, Pairing Function

Index entries for sequences related to sigma(n)

Formula

a(n) = (1/2)*(2 + ((A001511(n)+A000203(n))^2) - A001511(n) - 3*A000203(n)).

Prog

(PARI)
A000203(n) = sigma(n);
A001511(n) = (1+valuation(n, 2));
A286460(n) = (1/2)*(2 + ((A001511(n)+A000203(n))^2) - A001511(n) - 3*A000203(n));
for(n=1, 10000, write("b286460.txt", n, " ", A286460(n)));
(Scheme) (define (A286460 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A000203 n)) 2) (- (A001511 n)) (- (* 3 (A000203 n))) 2)))
(Python)
from sympy import divisor_sigma as D
def a001511(n): return bin(n)[2:][::-1].index("1") + 1
def T(n, m): return ((n + m)**2 - n - 3*m + 2)//2
def a(n): return T(a001511(n), D(n))
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, May 12 2017

Crossrefs

Cf. A000027, A286360.

Cf. A000593, A146076 (sequences matching to this filter), also A000203, A161942, A286260, A286357.

Sequence in context: A090099 A365486 A138809 * A317231 A237646 A288188

Adjacent sequences: A286457 A286458 A286459 * A286461 A286462 A286463

Keyword

nonn

Author

Antti Karttunen, May 10 2017

Status

approved