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A023662 Convolution of odd numbers and primes.

%I A023662 #26 Mar 04 2025 23:23:39
%S A023662 2,9,24,51,96,165,264,399,576,805,1094,1451,1886,2405,3014,3723,4544,
%T A023662 5485,6554,7761,9112,10615,12280,14117,16140,18361,20786,23421,26272,
%U A023662 29345,32658,36229,40068,44183,48586,53289,58300,63631,69292
%N A023662 Convolution of odd numbers and primes.
%F A023662 a(n) = Sum_{i=0..n-1} A000040(n-i)*A005408(i). - _R. J. Mathar_, Nov 29 2015
%F A023662 a(n) = Sum_{i=0..n-1} A061802(i). - _Marco Zárate_, Jun 09 2024
%F A023662 From _Ridouane Oudra_, Feb 19 2025: (Start)
%F A023662 a(n) = Sum_{i=1..n} Sum_{j=1..n} min(prime(i), prime(j)).
%F A023662 a(n) = A167214(n) - A062020(n).
%F A023662 a(n) = 2*A167214(n) - A316322(n).
%F A023662 a(n) = A014148(n) + A014148(n-1).
%F A023662 a(n) = A007504(n) + 2*A014148(n-1). (End)
%p A023662 A023662 := proc(n)
%p A023662     add( ithprime(n-i)*(2*i+1),i=0..n-1) ;
%p A023662 end proc: # _R. J. Mathar_, Nov 29 2015
%t A023662 Table[Sum[Prime[n - k + 1] (2 k - 1), {k, n}], {n, 39}] (* _Michael De Vlieger_, Nov 29 2015 *)
%o A023662 (PARI) a(n) = sum(i=1, n, prime(n-i+1)*(2*i-1)); \\ _Michel Marcus_, Sep 30 2013
%Y A023662 Cf. A000040, A005408, A061802 (first differences).
%Y A023662 Cf. A167214, A062020, A316322, A014148, A007504.
%K A023662 nonn
%O A023662 1,1
%A A023662 _Clark Kimberling_