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

Author

Antti Karttunen, May 10 2017

Keywords

• nonn

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)

Crossrefs

Cf. A000027, A286360.

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

Programs

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)));

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

Scheme

(define (A286460 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A000203 n)) 2) (- (A001511 n)) (- (* 3 (A000203 n))) 2)))

Formula

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