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