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

1,1

Links

Table of n, a(n) for n=1..39.

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)

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 *)

Prog

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

Crossrefs

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

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

Sequence in context: A294872 A006002 A259969 * A381632 A131357 A274543

Adjacent sequences: A023659 A023660 A023661 * A023663 A023664 A023665

Keyword

nonn

Author

Clark Kimberling

Status

approved