A337093 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.

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

Offset: 1

Author

Michel Marcus, Aug 15 2020

Keywords

• nonn

Crossrefs

Cf. A001055, A069016, A337080.

Programs

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]]);}
factorz(n) = factz(n, 2);
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, ", ")););}

Formula

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