OFFSET
1,4
COMMENTS
Second column of the array at A240181. Multiplicities greater than 1 are not counted; e.g. there is exactly one number that is in both {4,1,1} and {3,1,1,1}.
LINKS
Manfred Scheucher, Table of n, a(n) for n = 1..65
Manfred Scheucher, Sage Script
EXAMPLE
a(6) counts these 6 partitions: 51, 42, 411, 3111, 2211, 21111, of which the respective conjugates are 21111, 2211, 3111, 411, 42, 51.
MATHEMATICA
z = 30; p[n_, k_] := p[n, k] = IntegerPartitions[n][[k]]; c[p_] := c[p] = Table[Count[#, _?(# >= i &)], {i, First[#]}] &[p]; b[n_] := b[n] = Table[Intersection[p[n, k], c[p[n, k]]], {k, 1, PartitionsP[n]}]; Table[Count[Map[Length, b[n]], 0], {n, 1, z}] (* A240674 *)
Table[Count[Map[Length, b[n]], 1], {n, 1, z}] (* A240675 *)
PROG
(PARI) conjug(v) = {my(m = matrix(#v, vecmax(v))); for (i=1, #v, for (j=1, v[i], m[i, j] = 1; ); ); vector(vecmax(v), i, sum(j=1, #v, m[j, i])); }
a(n) = {my(v = partitions(n)); my(nb = 0); for (k=1, #v, if (#setintersect(Set(v[k]), Set(conjug(v[k]))) == 1, nb++); ); nb; } \\ Michel Marcus, Jun 02 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 12 2014
EXTENSIONS
More terms from Manfred Scheucher, Jun 01 2015
STATUS
approved