cp's OEIS Frontend

A174939 a(n) = Sum_{k<=n} A007955(k) * A007955(k) = Sum_{k<=n} A007955(k)^2, where A007955(m) = product of divisors of m.

%I A174939 #14 May 03 2022 21:15:49
%S A174939 1,5,14,78,103,1399,1448,5544,6273,16273,16394,3002378,3002547,
%T A174939 3040963,3091588,4140164,4140453,38152677,38153038,102153038,
%U A174939 102347519,102581775,102582304,110177896480,110177912105,110178369081,110178900522,110660790826,110660791667
%N A174939 a(n) = Sum_{k<=n} A007955(k) * A007955(k) = Sum_{k<=n} A007955(k)^2, where A007955(m) = product of divisors of m.
%H A174939 Michael S. Branicky, <a href="/A174939/b174939.txt">Table of n, a(n) for n = 1..10000</a>
%F A174939 a(n) = Sum_{k=1..n} A062758(k). - _Michel Marcus_, May 03 2022
%e A174939 For n = 4, A007955(n) = b(n): a(4) = b(1)^2 + b(2)^2 + b(3)^2 + b(4)^2 = 1^2 + 2^2 + 3^2 + 8^2 = 78.
%t A174939 Accumulate@ Array[#^DivisorSigma[0, #] &, 29] (* _Michael De Vlieger_, May 03 2022 *)
%o A174939 (PARI) a(n) = sum(k=1, n, k^numdiv(k)); \\ _Michel Marcus_, May 03 2022
%o A174939 (Python)
%o A174939 from sympy import divisor_count
%o A174939 from itertools import count, islice
%o A174939 def agen():
%o A174939     an = 1
%o A174939     for k in count(2):
%o A174939         yield an
%o A174939         an += k**divisor_count(k)
%o A174939 print(list(islice(agen(), 29))) # _Michael S. Branicky_, May 03 2022
%Y A174939 Cf. A007955, A062758.
%K A174939 nonn
%O A174939 1,2
%A A174939 _Jaroslav Krizek_, Apr 02 2010
%E A174939 a(27) and beyond from _Michael S. Branicky_, May 03 2022