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

1,4

Links

Table of n, a(n) for n=1..85.

Formula

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

Prog

(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, ", ")); ); }

Crossrefs

Cf. A001055, A069016, A337080.

Sequence in context: A252665 A001055 A335079 * A320266 A277692 A354992

Adjacent sequences: A337090 A337091 A337092 * A337094 A337095 A337096

Keyword

nonn

Author

Michel Marcus, Aug 15 2020

Status

approved