I am working on a counting function involving prime numbers and managed to construct a sage function that is correct:
def sum_X_subs(plist, plen):
psum = 0
for k in range(plen-1):
ptwo = 2^(plen-k) - 2
psum += sum(mul(psub)*ptwo for psub in Subsets(plist, k))
return psum
# end sum_X_subs
flist = []
plist = [5]; plen = 1
for p in prime_range(7, 41+1):
plist.append(p)
plen += 1
flist.append(sum_X_subs(plist, plen))
flist
# [2, 52, 1162, 28196, 712250, 20379100, 696733730, 25016026280, 1042543611410, 47439135073960]
Now I need a lower bounds function for this - a sum(product(subsets(set))). None of the literature I've found covers anything close to it. (I have a vague memory of an Euler project problem that involved subset products).