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A324923 Number of distinct factors in the factorization of n into factors q(i) = prime(i)/i, i > 0. 27
0, 1, 2, 1, 3, 2, 2, 1, 2, 3, 4, 2, 3, 2, 3, 1, 3, 2, 2, 3, 3, 4, 3, 2, 3, 3, 2, 2, 4, 3, 5, 1, 4, 3, 4, 2, 3, 2, 3, 3, 4, 3, 3, 4, 3, 3, 4, 2, 2, 3, 4, 3, 2, 2, 4, 2, 3, 4, 4, 3, 3, 5, 3, 1, 4, 4, 3, 3, 3, 4, 4, 2, 4, 3, 3, 2, 5, 3, 5, 3, 2, 4, 4, 3, 5, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Also the number of distinct proper terminal subtrees of the rooted tree with Matula-Goebel number n.

LINKS

Table of n, a(n) for n=1..87.

EXAMPLE

The factorization 22 = q(1)^2 q(2) q(3) q(5) has four distinct factors, so a(22) = 4.

MATHEMATICA

difac[n_]:=If[n==1, {}, With[{i=PrimePi[FactorInteger[n][[1, 1]]]}, Sort[Prepend[difac[n*i/Prime[i]], i]]]];

Table[Length[Union[difac[n]]], {n, 100}]

CROSSREFS

a(n) = A317713(n) - 1.

Cf. A000081, A003963, A061775, A109082, A109129, A120383, A196050.

Cf. A324850, A324922, A324924, A324925, A324931, A324934, A324935, A324936.

Sequence in context: A303639 A090000 A109082 * A126303 A306467 A157810

Adjacent sequences:  A324920 A324921 A324922 * A324924 A324925 A324926

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 20 2019

STATUS

approved

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Last modified May 19 16:36 EDT 2019. Contains 323395 sequences. (Running on oeis4.)