OFFSET
0,13
LINKS
FORMULA
a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m) * (n-i-j-k-l-m), where c = A010051.
MAPLE
N:= proc(m, k, n) option remember;
local q, t;
if m = 1 then if k=n and isprime(k) then return 1
else return 0
fi fi;
if m*k < n then return 0 fi;
t:= 0;
q:= ceil((n-k)/(m-1))-1;
do
q:= nextprime(q);
if q > min(k, n-k) then return t fi;
t:= t + procname(m-1, q, n-k)
od;
end proc:
F:= proc(n) local p, q, t;
p:= ceil(n/6)-1;
t:= 0;
do
p:= nextprime(p);
if p >= n then return t fi;
q:= ceil((n-p)/5)-1;
do
q:= nextprime(q);
if q > min(p, n-p) then break fi;
t:= t + p*N(5, q, n-p);
od
od
end proc:
map(F, [$0..100]); # Robert Israel, Jul 02 2019
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[(n - i - j - k - l - m)*(PrimePi[i] - PrimePi[i - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[l] - PrimePi[l - 1]) (PrimePi[m] - PrimePi[m - 1]) (PrimePi[n - i - j - k - l - m] - PrimePi[n - i - j - k - l - m - 1]), {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 30 2019
STATUS
approved