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Difference between the number of unordered factorizations and the number of distinct sums of terms in these unordered factorizations for those integers where this difference is positive.

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`%I #4 Aug 17 2020 22:42:48
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`%S 1,1,1,2,1,2,1,3,2,2,1,4,1,2,2,5,1,6,1,4,3,2,1,1,7,2,2,3,4,1,5,1,7,2,
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`%T 2,2,13,1,2,2,8,1,6,1,4,5,2,1,12,2,4,2,4,1,12,2,7,2,2,1,15,1,2,5,11,3,
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`%U 5,1,2,4,2,5,1,20,1,2,5,4,2,5,1,13,6,2,1
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`%N Difference between the number of unordered factorizations and the number of distinct sums of terms in these unordered factorizations for those integers where this difference is positive.
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`%F a(n) = A001055(A337080(n)) - A069016(A337080(n)).
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`%o (PARI) factz(n, minn) = {my(v=[]); fordiv(n, d, if ((d>=minn) && (d<=sqrtint(n)), w = factz(n/d, d); for (i=1, #w, w[i] = concat([d], w[i]);); v = concat(v, w););); concat(v, [[n]]);}
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`%o factorz(n) = factz(n, 2);
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`%o lista(nn) = {for (n=1, nn, my(vf = factorz(n)); my(vs = apply(x->vecsum(x), vf)); my(d = #vs - #Set(vs)); if (d>0, print1(d, ", ")););}
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`%Y Cf. A001055, A069016, A337080.
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`%K nonn
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`%O 1,4
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`%A _Michel Marcus_, Aug 15 2020
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