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A024321
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (composite numbers).
17
0, 0, 6, 8, 9, 10, 12, 14, 25, 28, 32, 35, 37, 40, 44, 46, 64, 69, 73, 77, 81, 85, 89, 93, 96, 100, 128, 133, 139, 144, 148, 154, 162, 166, 170, 176, 181, 187, 223, 229, 236, 242, 248, 255, 262, 268, 275, 281, 287, 294, 301, 308, 354, 361, 370, 380, 386, 394, 401, 408, 418, 425
OFFSET
1,3
LINKS
FORMULA
a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*A002808(n-j+1). - G. C. Greubel, Jan 19 2022
MATHEMATICA
A023531[n_]:= SquaresR[1, 8n+9]/2;
Composite[n_]:= FixedPoint[n +PrimePi[#] +1 &, n];
a[n_]:= Sum[A023531[j]*Composite[n-j+1], {j, Floor[(n+1)/2]}];
Table[a[n], {n, 70}] (* G. C. Greubel, Jan 19 2022 *)
PROG
(Magma)
A002808:= [n : n in [2..100] | not IsPrime(n) ];
A023531:= func< n | IsIntegral( (Sqrt(8*n+9) -3)/2 ) select 1 else 0 >;
[ (&+[A023531(j)*A002808[n-j+1]: j in [1..Floor((n+1)/2)]]) : n in [1..70]]; // G. C. Greubel, Jan 19 2022
(Sage)
A002808 = [n for n in (1..250) if sloane.A001222(n) > 1]
def A023531(n):
if ((sqrt(8*n+9) -3)/2).is_integer(): return 1
else: return 0
[sum( A023531(j)*A002808[n-j] for j in (1..floor((n+1)/2)) ) for n in (1..70)] # G. C. Greubel, Jan 19 2022
KEYWORD
nonn
STATUS
approved