A384396 Position of first appearance of n in A384389 (proper choices of disjoint strict partitions of each prime index).

1, 5, 11, 13, 17, 19, 62, 23, 111, 29, 123, 31, 129, 217, 37, 141, 106, 41, 159, 391, 118, 43

Offset

0,2

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

By "proper" we exclude the case of all singletons, which is disjoint when n is squarefree.

Links

Table of n, a(n) for n=0..21.

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
pofprop[y_]:=Select[DeleteCases[Join@@@Tuples[IntegerPartitions/@y], y], UnsameQ@@#&];
lv=Table[Length[pofprop[prix[n]]], {n, 100}];
mnrm[s_]:=If[Min@@s==1, mnrm[DeleteCases[s-1, 0]]+1, 0];
Table[Position[lv, x][[1, 1]], {x, 0, mnrm[lv+1]-1}]

Crossrefs

Positions of first appearances in A384389.

A000041 counts integer partitions, strict A000009.

A048767 is the Look-and-Say transform, fixed points A048768, counted by A217605.

A055396 gives least prime index, greatest A061395.

A056239 adds up prime indices, row sums of A112798.

A239455 counts Look-and-Say partitions, ranks A351294

A351293 counts non-Look-and-Say partitions, ranks A351295.

Cf. A382912, A383710, A382913, A383708.

Cf. A179009, A279790, A357982, A381454, A382525, A383706, A384321, A384322, A384347, A384349, A384390, A384393.

Sequence in context: A085909 A288450 A346416 * A371449 A272446 A307390

Adjacent sequences: A384393 A384394 A384395 * A384397 A384398 A384399

Keyword

nonn,more

Author

Gus Wiseman, Jun 03 2025

Status

approved