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A327525 Number of factorizations of A302569(n), the n-th number that is 1, prime, or whose prime indices are pairwise coprime. 0
1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 4, 1, 2, 2, 5, 1, 1, 4, 2, 1, 7, 2, 4, 1, 5, 1, 7, 2, 2, 2, 1, 2, 7, 1, 1, 4, 2, 1, 12, 2, 4, 1, 2, 7, 2, 1, 11, 1, 2, 11, 5, 1, 4, 2, 5, 1, 1, 2, 4, 2, 1, 12, 2, 1, 2, 2, 7, 1, 4, 2, 2, 2, 19, 1, 1, 5, 1, 7, 2, 1, 1, 5, 12, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
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.
LINKS
FORMULA
a(n) = A001055(A302569(n)).
EXAMPLE
The a(47) = 11 factorizations of 60 together with the corresponding multiset partitions of {1,1,2,3}:
(2*2*3*5) {{1},{1},{2},{3}}
(2*2*15) {{1},{1},{2,3}}
(2*3*10) {{1},{2},{1,3}}
(2*5*6) {{1},{3},{1,2}}
(2*30) {{1},{1,2,3}}
(3*4*5) {{2},{1,1},{3}}
(3*20) {{2},{1,1,3}}
(4*15) {{1,1},{2,3}}
(5*12) {{3},{1,1,2}}
(6*10) {{1,2},{1,3}}
(60) {{1,1,2,3}}
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, #]&]}]];
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
y=Select[Range[nn], PrimeQ[#]||CoprimeQ@@primeMS[#]&];
Table[Length[facsusing[Rest[y], n]], {n, y}]
CROSSREFS
See link for additional cross-references.
Sequence in context: A134583 A087467 A231568 * A327540 A227687 A128118
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 20 2019
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)