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!)
A316789 Number of same-tree-factorizations of n. 2
1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A constant factorization of n is a finite nonempty constant multiset of positive integers greater than 1 with product n. Constant factorizations correspond to perfect divisors (A089723). A same-tree-factorization of n is either (case 1) the number n itself or (case 2) a finite sequence of two or more same-tree-factorizations, one of each factor in a constant factorization of n.

a(n) depends only on the prime signature of n. - Andrew Howroyd, Nov 18 2018

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 1 + Sum_{n = x^y, y > 1} a(x)^y.

a(2^n) = A281145(n).

EXAMPLE

The a(64) = 14 same-tree-factorizations:

  64

  (8*8)

  (4*4*4)

  (8*(2*2*2))

  ((2*2*2)*8)

  (4*4*(2*2))

  (4*(2*2)*4)

  ((2*2)*4*4)

  (2*2*2*2*2*2)

  (4*(2*2)*(2*2))

  ((2*2)*4*(2*2))

  ((2*2)*(2*2)*4)

  ((2*2*2)*(2*2*2))

  ((2*2)*(2*2)*(2*2))

MATHEMATICA

a[n_]:=1+Sum[a[n^(1/d)]^d, {d, Rest[Divisors[GCD@@FactorInteger[n][[All, 2]]]]}]

Array[a, 100]

PROG

(PARI) a(n)={my(z, e=ispower(n, , &z)); 1 + if(e, sumdiv(e, d, if(d>1, a(z^(e/d))^d)))} \\ Andrew Howroyd, Nov 18 2018

CROSSREFS

Cf. A001055, A001597, A001678, A003238, A007916, A052409, A052410, A067824, A089723, A281118, A281145, A294336, A316790.

Sequence in context: A326028 A294338 A316790 * A319661 A320015 A241918

Adjacent sequences:  A316786 A316787 A316788 * A316790 A316791 A316792

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 14 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 September 29 14:13 EDT 2020. Contains 337431 sequences. (Running on oeis4.)