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a(n) = Sum_{k = 1..ceiling(n/2)} [d_3(k)*d_3(n+1-k)], where d_3 = A007425.
2

%I #13 Apr 19 2024 03:27:50

%S 0,1,3,12,15,30,36,75,64,108,102,198,147,237,201,361,255,435,318,552,

%T 417,630,459,963,537,888,696,1099,714,1302,810,1503,1044,1506,1000,

%U 2103,1119,1869,1443,2337,1344,2568,1464,2697,1884,2676,1710,3966,1839,3150,2400,3714,2115,4189,2292,4359,2943,4098

%N a(n) = Sum_{k = 1..ceiling(n/2)} [d_3(k)*d_3(n+1-k)], where d_3 = A007425.

%C For background references see A330570.

%H Amiram Eldar, <a href="/A331074/b331074.txt">Table of n, a(n) for n = 0..10000</a>

%t f[p_, e_] := (e+1)*(e+2)/2; s[1] = 1; s[n_] := s[n] = Times @@ f @@@ FactorInteger[n]; a[n_ := Sum[s[k] * s[n+1-k], {k, 1, Ceiling[n/2]}]; Array[a, 100, 0] (* _Amiram Eldar_, Apr 19 2024 *)

%Y Cf. A007425.

%Y See A331073 for another version.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jan 10 2020

%E Offset and name corrected by _Amiram Eldar_, Apr 19 2024