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a(n) = Sum_{k<=n} A007955(k) * A007955(n-k+1), where A007955(m) = product of divisors of m.
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%I #6 Aug 06 2024 02:08:07

%S 1,4,10,28,51,140,252,452,953,1164,2974,5676,13531,14828,40744,27260,

%T 146845,55372,288174,177700,574867,204916,3721652,988332,3550621,

%U 3267452,11129590,4173196,46286551,7402156,77215116,27553508,97906405,20169220,1259249286,43886132

%N a(n) = Sum_{k<=n} A007955(k) * A007955(n-k+1), where A007955(m) = product of divisors of m.

%e For n = 4, A007955(n) = b(n): a(4) = b(1)*b(4) + b(2)*b(3) + b(3)* b(2) + b(4)*b(1) = 1*8 + 2*3 + 3*2 + 8*1 = 28.

%t s[n_] := n^(DivisorSigma[0, n]/2); a[n_] := Sum[s[k] * s[n-k+1], {k, 1, n}]; Array[a, 50] (* _Amiram Eldar_, Aug 06 2024 *)

%Y Cf. A007955.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Apr 02 2010

%E More terms from _Amiram Eldar_, Aug 06 2024