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A327533 Number of factorizations of the n-th number that is 1 or whose prime indices are relatively prime A289509(n - 1) into numbers > 1 satisfying the same conditions. 0
1, 1, 2, 1, 3, 1, 2, 1, 1, 5, 1, 2, 1, 4, 1, 2, 2, 7, 1, 1, 1, 3, 1, 4, 1, 2, 1, 1, 7, 1, 1, 2, 1, 1, 4, 1, 5, 1, 11, 2, 2, 1, 2, 6, 1, 1, 2, 1, 1, 7, 1, 3, 1, 1, 4, 3, 2, 1, 1, 1, 12, 1, 1, 3, 2, 4, 1, 1, 3, 2, 7, 1, 2, 1, 1, 10, 1, 1, 2, 1, 15, 1, 5, 1, 1, 4 (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. Numbers whose prime indices are relatively prime are A289509.

LINKS

Table of n, a(n) for n=1..86.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

EXAMPLE

The a(76) = 10 factorizations of 120 into elements of A289509 together with the corresponding multiset partitions of {1,1,1,2,3}:

  (2*2*2*15)  {{1},{1},{1},{2,3}}

  (2*2*30)    {{1},{1},{1,2,3}}

  (2*4*15)    {{1},{1,1},{2,3}}

  (2*6*10)    {{1},{1,2},{1,3}}

  (2*60)      {{1},{1,1,2,3}}

  (4*30)      {{1,1},{1,2,3}}

  (6*20)      {{1,2},{1,1,3}}

  (8*15)      {{1,1,1},{2,3}}

  (10*12)     {{1,3},{1,1,2}}

  (120)       {{1,1,1,2,3}}

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, #]&]}]];

y=Select[Range[nn], #==1||GCD@@PrimePi/@First/@FactorInteger[#]==1&];

Table[Length[facsusing[Rest[y], n]], {n, y}]

CROSSREFS

See link for additional cross-references.

Cf. A001055, A006530, A112798, A281116, A289509, A318721.

Sequence in context: A028293 A092782 A228098 * A327518 A174532 A089242

Adjacent sequences:  A327530 A327531 A327532 * A327534 A327535 A327536

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 17 2019

STATUS

approved

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)