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A024328
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a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*prime(n-j+1).
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3
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0, 0, 3, 5, 7, 11, 13, 17, 30, 36, 46, 50, 60, 70, 74, 84, 117, 131, 139, 157, 171, 177, 193, 207, 221, 237, 294, 310, 330, 348, 360, 390, 408, 424, 448, 470, 486, 506, 611, 625, 653, 673, 699, 739, 761, 781, 803, 835, 863, 891, 925, 953, 1078, 1104, 1136, 1180, 1214, 1244, 1270
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*prime(n-j+1).
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MATHEMATICA
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Table[t=0; m=3; p=BitShiftRight[n]; n--; While[n>p, t += Prime[n]; n -= m++]; t, {n, 120}] (* G. C. Greubel, Feb 17 2022 *)
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PROG
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(Magma)
b:= func< n, j | IsIntegral((Sqrt(8*j+9) -3)/2) select NthPrime(n-j+1) else 0 >;
A024328:= func< n | (&+[b(n, j): j in [1..Floor((n+1)/2)]]) >;
(Sage)
def b(n, j): return nth_prime(n-j+1) if ((sqrt(8*j+9) -3)/2).is_integer() else 0
@CachedFunction
def A024327(n): return sum( b(n, j) for j in (1..floor((n+1)/2)) )
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CROSSREFS
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Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024318, A024319, A024320, A024321, A024322, A024323, A024324, A024325, A024326, A024327.
Cf. A023531 (characteristic function of {n(n+3)/2}).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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