A023662 Convolution of odd numbers and primes.

2, 9, 24, 51, 96, 165, 264, 399, 576, 805, 1094, 1451, 1886, 2405, 3014, 3723, 4544, 5485, 6554, 7761, 9112, 10615, 12280, 14117, 16140, 18361, 20786, 23421, 26272, 29345, 32658, 36229, 40068, 44183, 48586, 53289, 58300, 63631, 69292

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A000040, A005408, A061802 (first differences).

Cf. A167214, A062020, A316322, A014148, A007504.

Programs

Maple

A023662 := proc(n)
    add( ithprime(n-i)*(2*i+1),i=0..n-1) ;
end proc: # R. J. Mathar, Nov 29 2015

Mathematica

Table[Sum[Prime[n - k + 1] (2 k - 1), {k, n}], {n, 39}] (* Michael De Vlieger, Nov 29 2015 *)

PARI

a(n) = sum(i=1, n, prime(n-i+1)*(2*i-1)); \\ Michel Marcus, Sep 30 2013

Formula

a(n) = Sum_{i=0..n-1} A000040(n-i)*A005408(i). - R. J. Mathar, Nov 29 2015

a(n) = Sum_{i=0..n-1} A061802(i). - Marco Zárate, Jun 09 2024

From Ridouane Oudra, Feb 19 2025: (Start)

a(n) = Sum_{i=1..n} Sum_{j=1..n} min(prime(i), prime(j)).

a(n) = A167214(n) - A062020(n).

a(n) = 2*A167214(n) - A316322(n).

a(n) = A014148(n) + A014148(n-1).

a(n) = A007504(n) + 2*A014148(n-1). (End)