A286359 Compound filter: a(n) = P(sigma(n), sigma(2n)), where P(n,k) is sequence A000027 used as a pairing function, and sigma is the sum of divisors (A000203).

4, 39, 109, 217, 259, 753, 473, 1005, 1288, 1729, 1093, 3769, 1499, 3105, 4489, 4309, 2503, 8295, 3101, 8557, 8033, 7057, 4489, 16713, 7534, 9633, 12601, 15281, 7051, 28513, 8033, 17829, 18193, 15985, 18193, 40561, 11363, 19761, 24809, 37765, 13903, 50817, 15269, 34537, 48283, 28513, 18193, 70249, 25708, 47679, 41113, 47069, 23059, 79521, 41113, 67281, 50801

Offset

1,1

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 + ((A000203(n)+A000203(2*n))^2) - A000203(n) - 3*A000203(2*n)).

Prog

(PARI)
A000203(n) = sigma(n);
A286359(n) = (1/2)*(2 + ((A000203(n)+A000203(n+n))^2) - A000203(n) - 3*A000203(n+n));
for(n=1, 10000, write("b286359.txt", n, " ", A286359(n)));
(Scheme) (define (A286359 n) (* (/ 1 2) (+ (expt (+ (A000203 n) (A000203 (* 2 n))) 2) (- (A000203 n)) (- (* 3 (A000203 (* 2 n)))) 2)))
(Python)
from sympy import divisor_sigma as D
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a(n): return T(D(n), D(2*n)) # Indranil Ghosh, May 12 2017

Crossrefs

Cf. A000027, A286360, A286460.

Cf. A000203, A002131, A054785 (sequences matching to this filter), also A161942, A286357.

Sequence in context: A278052 A093850 A297736 * A201740 A024212 A006408

Adjacent sequences: A286356 A286357 A286358 * A286360 A286361 A286362

Keyword

nonn

Author

Antti Karttunen, May 10 2017

Status

approved