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A023672 Convolution of A023533 and primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 2 09:41 EST 2023. Contains 360004 sequences. (Running on oeis4.)