login
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.
0

%I #4 Aug 17 2020 22:42:48

%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,

%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,

%U 5,1,2,4,2,5,1,20,1,2,5,4,2,5,1,13,6,2,1

%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.

%F a(n) = A001055(A337080(n)) - A069016(A337080(n)).

%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]]);}

%o factorz(n) = factz(n, 2);

%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, ", ")););}

%Y Cf. A001055, A069016, A337080.

%K nonn

%O 1,4

%A _Michel Marcus_, Aug 15 2020