A067459 - OEIS

%I #16 Jan 10 2021 05:55:16

%S 0,0,1,7,17,15,43,58,66,90,189,211,273,336,431,398,588,689,910,872,

%T 1199,1435,1438,1862,2007,2079,2208,2764,3329,2964,4356,3945,4359,

%U 4633,5330,5855,6210,7491,7821,7406,9610,9373,10309,10606,11965,12362,12468

%N Sum of the remainders when n^2 is divided by squares less than n.

%H Robert Israel, <a href="/A067459/b067459.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{k=1..n-1} (n^2 mod k^2). [From _Robert Israel_, Jan 07 2021 Maple program.]

%p f:= proc(n) local k; add(n^2 mod k^2,k=2..n-1) end proc:

%p map(f, [$1..100]); # _Robert Israel_, Jan 07 2021

%t Table[ Apply[ Plus, Mod[n^2, Table[i^2, {i, 1, n - 1} ]]], {n, 1, 50} ]

%o (PARI) a(n) = sum(k=1, n-1, n^2 % k^2); \\ _Michel Marcus_, Jan 09 2021

%Y Cf. A000290.

%K easy,nonn

%O 1,4

%A _Amarnath Murthy_, Feb 07 2002

%E Edited and extended by _Robert G. Wilson v_, Feb 08 2002