A263097 - OEIS

%I #10 Oct 11 2015 10:58:53

%S 0,1,0,1,1,2,0,1,3,3,2,3,8,2,7,5,10,20,16,14,22,19,17,8,46,12,11,53,

%T 44,75,63,56,50,130,38,71,33,191,161,270,227,201,181,467,138,256,347,

%U 509,362,491,1045,368,513,1251,747,1927,568,1057,1431,2097,1494,2025,4308,2946,687,6093,4167,8399,1189,1287,4605,6239,9141,6513,8822,18782,15834,26561,22392,37564,16401,32375,17317,12602

%N First differences of A263096.

%C a(n) = number of perfect squares in range [A002182(n)+1 .. A002182(n+1)].

%H Antti Karttunen, <a href="/A263097/b263097.txt">Table of n, a(n) for n = 1..999</a> (based on the b-file of A002182 provided by _T. D. Noe_.)

%F a(n) = A263096(n+1) - A263096(n).

%e A002182 begins as 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ...

%e In range [2,2] there are no squares, so a(1) = 0.

%e In range [3,4] there is one square, so a(2) = 1.

%e In range [5,6] there are no squares, so a(3) = 0.

%e In range [7,12] there is one square, so a(4) = 1.

%e In range [13,24] there is one square, so a(5) = 1.

%e In range [25,36] there are two squares, so a(6) = 2.

%e In range [37,48] there are no squares, so a(7) = 0.

%e In range [49,60] there is one square, so a(8) = 1.

%e In range [61,120] there are three squares (64, 81, 100), thus a(9) = 3.

%o (Scheme) (define (A263097 n) (- (A263096 (+ n 1)) (A263096 n)))

%Y Cf. A000196, A002182, A263096, A263098.

%K nonn

%O 1,6

%A _Antti Karttunen_, Oct 10 2015