|
| |
|
|
A327520
|
|
Number of factorizations of the n-th stable number A316476(n) into stable numbers > 1.
|
|
0
|
|
|
|
1, 1, 2, 1, 1, 3, 2, 1, 1, 2, 5, 1, 1, 1, 2, 3, 1, 1, 7, 2, 2, 1, 1, 1, 4, 1, 2, 2, 1, 2, 1, 1, 11, 1, 2, 1, 1, 4, 2, 1, 5, 1, 2, 1, 2, 2, 2, 1, 4, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 15, 1, 7, 1, 1, 2, 2, 2, 1, 1, 4, 2, 1, 2, 1, 5, 1, 2, 1, 4, 2, 1, 1, 2, 1, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
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. A number is stable if its distinct prime indices are pairwise indivisible. Stable numbers are listed in A316476.
|
|
|
LINKS
|
Table of n, a(n) for n=1..86.
Gus Wiseman, Sequences counting and encoding certain classes of multisets
|
|
|
EXAMPLE
|
The a(26) = 4 factorizations of 45 into stable numbers:
(3*3*5)
(3*15)
(5*9)
(45)
The a(201) = 11 multiset partitions of the prime indices of 495 into stable multisets:
{{2},{2},{3},{5}}
{{2},{2},{3,5}}
{{2},{3},{2,5}}
{{2},{5},{2,3}}
{{2},{2,3,5}}
{{3},{2,2},{5}}
{{3},{2,2,5}}
{{2,2},{3,5}}
{{5},{2,2,3}}
{{2,3},{2,5}}
{{2,2,3,5}}
|
|
|
MATHEMATICA
|
nn=100;
facsusing[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsusing[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
y=Select[Range[nn], stableQ[PrimePi/@First/@FactorInteger[#], Divisible]&];
Table[Length[facsusing[Rest[y], n]], {n, y}]
|
|
|
CROSSREFS
|
See link for additional cross-references.
Cf. A001055, A303362, A305149.
Sequence in context: A254111 A234246 A006375 * A184441 A172279 A348285
Adjacent sequences: A327517 A327518 A327519 * A327521 A327522 A327523
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Gus Wiseman, Sep 15 2019
|
|
|
STATUS
|
approved
|
| |
|
|
