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Sum of square roots of square divisors of n <= sqrt(n).
3

%I #16 Aug 19 2021 08:52:06

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,

%T 1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,

%U 1,1,1,3,1,1,1,3,1,1,1,3,4,1,1,3,1,1,1,3,1,4,1,3,1,1,1,3,1,1,4,3,1,1,1,3,1

%N Sum of square roots of square divisors of n <= sqrt(n).

%H Antti Karttunen, <a href="/A069292/b069292.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>

%F G.f.: Sum_{k>=1} k * x^(k^4) / (1 - x^(k^2)). - _Ilya Gutkovskiy_, Aug 19 2021

%t Table[DivisorSum[n, Sqrt@ # &, And[IntegerQ@ Sqrt@ #, # <= Sqrt@ n] &], {n, 105}] (* _Michael De Vlieger_, Nov 20 2017 *)

%o (PARI) A069292(n) = { my(r="NA"); sumdiv(n, d, (issquare(d,&r)&&((d^2)<=n))*r); } \\ _Antti Karttunen_, Nov 20 2017

%Y Cf. A035316, A046951, A000188, A069290, A069291, A069293.

%K nonn

%O 1,16

%A _Reinhard Zumkeller_, Mar 14 2002

%E More terms from _Antti Karttunen_, Nov 20 2017