A277191 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 odd.

0, 2, 2, 4, 5, 5, 7, 7, 9, 10, 10, 13, 12, 15, 16, 15, 18, 19, 20, 20, 24, 21, 25, 26, 26, 27, 30, 30, 31, 33, 33, 33, 37, 37, 38, 40, 42, 41, 43, 44, 46, 46, 48, 47, 51, 50, 51, 55, 53, 56, 57, 58, 61, 61, 64, 61, 63, 66, 69, 65, 68, 71, 73, 70, 74, 75, 76, 77, 79, 79, 81, 85, 80, 86, 85, 85, 89, 90, 91, 91, 92, 95, 95, 98, 95, 100

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, A277192.

After the initial zero, one more than A277193.

Programs

Scheme

(define (A277191 n) (add (lambda (i) (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} A000035(A002828(i)).

For all n >= 0, a(n) + A277192(n) = 2n+1.

For all n >= 1, a(n) = 1 + A277193(n).