cp's OEIS Frontend

A368058 Sum of the smaller parts of the partitions of n into two distinct parts with larger part prime.

%I A368058 #11 Jan 26 2024 11:30:03
%S A368058 0,0,1,1,2,1,2,4,6,3,4,6,8,4,6,8,10,13,16,20,24,17,20,24,28,19,22,25,
%T A368058 28,32,36,41,46,34,38,42,46,32,36,40,44,49,54,60,66,49,54,60,66,72,78,
%U A368058 84,90,97,104,111,118,96,102,109,116,93,100,107,114,121,128,136,144,152,160
%N A368058 Sum of the smaller parts of the partitions of n into two distinct parts with larger part prime.
%H A368058 Robert Israel, <a href="/A368058/b368058.txt">Table of n, a(n) for n = 1..10000</a>
%H A368058 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A368058 a(n) = Sum_{i=1..floor((n-1)/2)} i * c(n - i), where c is the prime characteristic (A010051).
%F A368058 a(n) = n*A294602(n) - A294487(n). - _Wesley Ivan Hurt_, Dec 09 2023
%p A368058 N:= 100: # for a(1) .. a(N)
%p A368058 V:= Vector(N):
%p A368058 for i from 1 do
%p A368058   p:= ithprime(i);
%p A368058   if p >= N then break fi;
%p A368058   m:= min(2*p-1,N);
%p A368058   V[p+1..m]:= V[p+1..m] + <$1..m-p>
%p A368058 od:
%p A368058 convert(V,list); # _Robert Israel_, Jan 26 2024
%t A368058 Table[Sum[i (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n - 1)/2]}],{n, 100}]
%Y A368058 Cf. A010051, A294111, A294487, A294602.
%K A368058 nonn
%O A368058 1,5
%A A368058 _Wesley Ivan Hurt_, Dec 09 2023