A277193 - OEIS

%I #12 Oct 05 2016 10:19:30

%S 0,1,1,3,4,4,6,6,8,9,9,12,11,14,15,14,17,18,19,19,23,20,24,25,25,26,

%T 29,29,30,32,32,32,36,36,37,39,41,40,42,43,45,45,47,46,50,49,50,54,52,

%U 55,56,57,60,60,63,60,62,65,68,64,67,70,72,69,73,74,75,76,78,78,80,84,79,85,84,84,88,89,90,90,91,94,94,97,94,99

%N Number of integers k in range [n^2, ((n+1)^2)-1] for which 3 = the least number of squares that add up to k (A002828).

%H Antti Karttunen, <a href="/A277193/b277193.txt">Table of n, a(n) for n = 0..512</a>

%F Sum_{i=n^2 .. ((n+1)^2)-1} (1-A010052(i))*(1-A229062(i))*(1-A072401(i)).

%F Other identities. For all n >= 0:

%F 1 + A077773(n) + a(n) + A277194(n) = 2n+1.

%F For n >= 1, a(n) = A277191(n)-1.

%o (Scheme)

%o (define (A277193 n) (add (lambda (i) (* (- 1 (A010052 i)) (- 1 (A229062 i)) (- 1 (A072401 i)))) (A000290 n) (+ -1 (A000290 (+ 1 n)))))

%o ;; Implements sum_{i=lowlim..uplim} intfun(i)

%o (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

%Y Cf. A000290, A002828, A010052, A072401, A077773, A229062, A277194.

%Y After the initial zero, one less than A277191.

%K nonn

%O 0,4

%A _Antti Karttunen_, Oct 04 2016