A224834 - OEIS

%I #23 Aug 29 2023 04:19:28

%S 1,1,1,5,1,5,1,5,5,5,1,9,1,5,5,14,1,9,1,14,5,5,1,18,5,5,5,14,1,13,1,

%T 14,5,5,5,34,1,5,5,18,1,25,1,14,9,5,1,34,5,9,5,14,1,25,5,18,5,5,1,38,

%U 1,5,9,30,5,25,1,14,5,13,1,50,1,5,9

%N a(n) = Sum {d|n, d <= n^(1/2)} tau(d)^2.

%H Robert Israel, <a href="/A224834/b224834.txt">Table of n, a(n) for n = 1..10000</a>

%F If p is prime, a(p^k) = A000330(1+floor(k/2)). - _Robert Israel_, Nov 30 2016

%p f:= proc(n) add(numtheory:-tau(d)^2, d = select(t -> (t^2<=n), numtheory:-divisors(n))) end proc:

%p map(f, [$1..100]); # _Robert Israel_, Nov 30 2016

%t a[n_] := DivisorSum[n, DivisorSigma[0, #]^2 &, #^2 <= n &]; Array[a, 100] (* _Amiram Eldar_, Aug 29 2023 *)

%o (PARI) a(n) = sumdiv(n, d, (d<=sqrtn(n, 2))*numdiv(d)^2) \\ _Michel Marcus_, Jul 21 2013

%o (PARI) a(n)=my(s=sqrtint(n)); sumdiv(n,d,if(d<=s,numdiv(d)^2)) \\ _Charles R Greathouse IV_, Jul 22 2013

%Y Cf. A000330, A007425, A062367, A224835.

%K nonn

%O 1,4

%A _Michel Marcus_, Jul 21 2013