login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A316979 Number of strict factorizations of n into factors > 1 with no equivalent primes. 7
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 2, 3, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 5, 1, 1, 1, 3, 3, 1, 1, 7, 1, 3, 1, 3, 1, 5, 1, 5, 1, 1, 1, 6, 1, 1, 3, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 3, 3, 1, 1, 1, 7, 2, 1, 1, 6, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

In a factorization, two primes are equivalent if each factor has in its prime factorization the same multiplicity of both primes. For example, in 60 = (2*30) the primes {3, 5} are equivalent but {2, 3} and {2, 5} are not.

LINKS

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

FORMULA

a(prime^n) = A000009(n).

EXAMPLE

The a(24) = 5 factorizations are (2*3*4), (2*12), (3*8), (4*6), (24).

The a(36) = 4 factorizations are (2*3*6), (2*18), (3*12), (4*9).

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];

dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}];

Table[Length[Select[facs[n], And[UnsameQ@@#, UnsameQ@@dual[primeMS/@#]]&]], {n, 100}]

CROSSREFS

Cf. A000009, A001055, A007716, A007717, A020555, A045778, A130091, A162247, A281116.

Cf. A316974, A316978, A316980, A316981.

Sequence in context: A115621 A326514 A077565 * A331024 A115561 A115622

Adjacent sequences:  A316976 A316977 A316978 * A316980 A316981 A316982

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 18 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 31 15:41 EDT 2020. Contains 334748 sequences. (Running on oeis4.)