\\ A PARI-program to compute terms of A014649 quickly. This works at least in GP/PARI CALCULATOR Version 2.9.4
\\ To run the program, just say read("a014649.gp.txt") in PARI.

\\ Based on David A. Corneth's PARI-program given at https://oeis.org/A066874/a066874.gp.txt
\\ (But note that the routine customparts is different here!)

\\ Antti Karttunen just provided the routine nonprimepower_divisors_with1
\\
\\ To produce a b-file, say:
\\
\\ allocatemem(2^30);
\\ default(parisizemax,2^31);
\\ for(n=1,20000,write("b014649.txt", n, " ", A014649(n)));
\\


A014649(n) = (customparts(nonprimepower_divisors_with1(n), n-1)[n]);

nonprimepower_divisors_with1(n) = vecsort(select(d -> ((1==d) || !isprimepower(d)), divisors(n)));


addhelp(customparts, "Vector of n+1 of number of partitions of 0 through n into parts of v. Assumes distinct elements in v.")
customparts(v, n) = {
	my(res = vector(n+1)); res[1] = 1; 
	for(i = 1, #v, 
	for(j = v[i]+1, n+1,
	res[j] += res[j - v[i]]
	)
	); res
}

custompartsIterate(n) = {
	my(v = vector(n, i, 1), s = sum(i = 1, n, vpartsCopy[v[i]]));
	while(v != 0, 
		j = 0; 
		s = sum(i=1,#v,vpartsCopy[v[i]]);
		if(s < maxSum, 
			mapisdefined(vInv, maxSum - s, &j); 
			if(j >= v[#v],
				count++
			);
			v = nxtVl(v, #vpartsCopy); 	
		,
			v = nxtVs(v)
		)
	)
}

nxtVl(v, {u = oo}) = {
if(v[#v] + 1 <= u, 
v[#v]++; v
,
nxtVs(v)
)
}

nxtVs(v) = {
forstep(j = #v - 1, 1, -1,
 if(v[j] + 1 < v[#v],
 v[j]++;
 for(k = j + 1, #v,
  v[k] = v[j] 
 );
 return(v)
)
) ; return([0])
}