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def g(n, k):
def g(n, k): return (0 if n > k else 1) + (0 if isprime(n) else sum([0 if d>k else g(n//d, d) for d in divisors(n)[1:-1]] if d <= k))
p = reduce(mul, [(prime(t + 1)**l[t] for t in range(len(l))]))
else:
else: return 0 if i<1 else sum([b(n - i*j, i - 1, l + [i]*j) for j in range(n//i + 1)])
def a(n): return b(n, n, [])
return b(n, n, [])
for n in range(1, 11): print (a(n) ) # Indranil Ghosh, Aug 19 2017, after Maple code
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Andrew Howroyd, <a href="/A035310/b035310.txt">Table of n, a(n) for n = 1..50</a>
1, 4, 12, 47, 170, 750, 3255, 16010, 81199, 448156, 2579626, 15913058, 102488024, 698976419, 4976098729, 37195337408, 289517846210, 2352125666883, 19841666995265, 173888579505200, 1577888354510786, 14820132616197925, 143746389756336173, 1438846957477988926
(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
D(p, n)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); my(u=EulerT(v)); Vec(1/prod(k=1, n, 1 - u[k]*x^k + O(x*x^n))-1, -n)/prod(i=1, #v, i^v[i]*v[i]!)}
seq(n)={my(s=0); forpart(p=n, s+=D(p, n)); s} \\ Andrew Howroyd, Dec 30 2020
nonn,more,nice
Terms a(16) and beyond from Andrew Howroyd, Dec 30 2020
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