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%I #14 Apr 19 2024 03:26:29
%S 1,4,10,16,25,34,44,64,82,91,109,127,136,163,208,223,241,259,277,331,
%T 358,367,397,457,475,505,565,583,610,637,658,721,748,775,883,919,928,
%U 955,1045,1075,1102,1129,1147,1255,1309,1318,1363,1453,1489,1543,1597,1615,1645,1735,1825,1915,1942,1951,2005,2059
%N a(n) = Sum_{i=1..n} d_3(i)*d_3(i+1)/3, where d_3(n) = A007425(n).
%C For background references see A330570.
%H Seiichi Manyama, <a href="/A331081/b331081.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A331080(n) / 3. - _Amiram Eldar_, Apr 19 2024
%t f[p_, e_] := (e+1)*(e+2)/2; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; With[{t = Array[s, 100]}, Accumulate[Most[t] * Rest[t]] / 3] (* _Amiram Eldar_, Apr 19 2024 *)
%Y Cf. A007425, A331080.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jan 10 2020