A024328 a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*prime(n-j+1).

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

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}).

Programs

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)]]) >;
[A024328(n) : n in [1..120]]; // G. C. Greubel, Feb 17 2022

Mathematica

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 *)

PARI

A024328(n)=sum(j=1, (n+1)\2, A023531(j)*prime(n-j+1)) \\ M. F. Hasler, Apr 12 2018

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)) )
[A024327(n) for n in (1..120)] # G. C. Greubel, Feb 17 2022

Formula

a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*prime(n-j+1).

Extensions

Name edited by M. F. Hasler, Apr 12 2018