A277192 Number of integers k in range [n^2, ((n+1)^2)-1] for which the least number of squares that add up to k (A002828) is even.

1, 1, 3, 3, 4, 6, 6, 8, 8, 9, 11, 10, 13, 12, 13, 16, 15, 16, 17, 19, 17, 22, 20, 21, 23, 24, 23, 25, 26, 26, 28, 30, 28, 30, 31, 31, 31, 34, 34, 35, 35, 37, 37, 40, 38, 41, 42, 40, 44, 43, 44, 45, 44, 46, 45, 50, 50, 49, 48, 54, 53, 52, 52, 57, 55, 56, 57, 58, 58, 60, 60, 58, 65, 61, 64, 66, 64, 65, 66, 68, 69, 68, 70, 69

Offset: 0

Author

Antti Karttunen, Oct 04 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..512

Crossrefs

Cf. A000035, A000290, A002828, A077773, A277191, A277194.

Programs

Scheme

(define (A277192 n) (add (lambda (i) (- 1 (A000035 (A002828 i)))) (A000290 n) (+ -1 (A000290 (+ 1 n)))))
;; Implements sum_{i=lowlim..uplim} intfun(i)
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

Formula

a(n) = Sum_{i=n^2 .. ((n+1)^2)-1} (1-A000035(A002828(i))).

For all n >= 0, A277191(n) + a(n) = 2n+1.

For n >= 1, a(n) = A077773(n) + A277194(n).