A286359 - OEIS

%I #14 May 12 2017 05:41:40

%S 4,39,109,217,259,753,473,1005,1288,1729,1093,3769,1499,3105,4489,

%T 4309,2503,8295,3101,8557,8033,7057,4489,16713,7534,9633,12601,15281,

%U 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

%N 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).

%H Antti Karttunen, <a href="/A286359/b286359.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

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

%o (PARI)

%o A000203(n) = sigma(n);

%o A286359(n) = (1/2)*(2 + ((A000203(n)+A000203(n+n))^2) - A000203(n) - 3*A000203(n+n));

%o for(n=1, 10000, write("b286359.txt", n, " ", A286359(n)));

%o (Scheme) (define (A286359 n) (* (/ 1 2) (+ (expt (+ (A000203 n) (A000203 (* 2 n))) 2) (- (A000203 n)) (- (* 3 (A000203 (* 2 n)))) 2)))

%o (Python)

%o from sympy import divisor_sigma as D

%o def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

%o def a(n): return T(D(n), D(2*n)) # _Indranil Ghosh_, May 12 2017

%Y Cf. A000027, A286360, A286460.

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

%K nonn

%O 1,1

%A _Antti Karttunen_, May 10 2017