A023672 Convolution of A023533 and primes.

2, 3, 5, 9, 14, 18, 24, 30, 36, 48, 53, 65, 77, 85, 97, 111, 121, 131, 149, 163, 174, 192, 204, 220, 242, 260, 272, 294, 310, 320, 350, 364, 382, 410, 436, 453, 469, 495, 513, 543, 569, 587, 615, 647, 661, 687, 715, 739, 759, 799, 827, 855, 869

Offset

1,1

Links

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

Formula

a(n) = Sum_{j=1..n} A000040(j) * A023533(n-j+1).

a(n) = Sum_{j=1..n} A000040(k + binomial(n+3, 3) - binomial(j+2, 3)), for 1 <= k <= binomial(n+2, 2), n >= 1 (as an irregular triangle). - G. C. Greubel, Jul 18 2022

Mathematica

A023672[n_, m_]:= A023672[n, m]= Sum[Prime[(m +Binomial[n+2, 3] -Binomial[j+2, 3])], {j, n}];
Table[A023672[n, m], {n, 10}, {m, Binomial[n+2, 2]}]//Flatten (* G. C. Greubel, Jul 18 2022 *)

Prog

(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[NthPrime(k)*A023533(n+1-k): k in [1..n]]): n in [1..100]]; // G. C. Greubel, Jul 18 2022
(SageMath)
def A023672(n, k): return sum(nth_prime(k +binomial(n+2, 3) -binomial(j+2, 3)) for j in (1..n))
flatten([[A023672(n, k) for k in (1..binomial(n+2, 2))] for n in (1..10)]) # G. C. Greubel, Jul 18 2022

Crossrefs

Cf. A000040, A023533.

Sequence in context: A195667 A005244 A058541 * A023567 A076027 A280204

Adjacent sequences: A023669 A023670 A023671 * A023673 A023674 A023675

Keyword

nonn

Author

Clark Kimberling

Status

approved