A316782 -id:A316782 - cp's OEIS frontend

A067039 The tower function n^{(n-1)!}.

1, 2, 9, 4096, 59604644775390625

Offset: 1

Amarnath Murthy, Dec 29 2001

nonn

a(n) = n^(n-1)^(n-2)^...^3^2^1 with all power operators nested from the left. Nesting from the right gives A049384. - Gus Wiseman, Jul 03 2019

			a(4) = 4^(3!) = 4^6 = 4096.

Cf. A000142, A007489, A049384, A052409, A052410, A140319, A294338, A316782, A325624.

makelist((n+1)^(n!),n,0,6); /* Martin Ettl, Jan 17 2013 */

A316784 Number of orderless identity tree-factorizations of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 1, 10, 1, 2, 2, 4, 1, 8, 1, 6, 2, 2, 2, 13, 1, 2, 2, 10, 1, 8, 1, 4, 4, 2, 1, 26, 1, 4, 2, 4, 1, 10, 2, 10, 2, 2, 1, 28, 1, 2, 4, 13, 2, 8, 1, 4, 2, 8, 1, 46, 1, 2, 4, 4, 2, 8, 1, 26, 3, 2, 1

Offset: 1

Gus Wiseman, Jul 13 2018

nonn

A factorization of n is a finite nonempty multiset of positive integers greater than 1 with product n. An orderless identity tree-factorization of n is either (case 1) the number n itself or (case 2) a finite set of two or more distinct orderless identity tree-factorizations, one of each factor in a factorization of n.

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

			The a(24)=10 orderless identity tree-factorizations:
  24
  (4*6)
  (3*8)
  (2*12)
  (2*3*4)
  (4*(2*3))
  (3*(2*4))
  (2*(2*6))
  (2*(3*4))
  (2*(2*(2*3)))

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

Cf. A001055, A001678, A004111, A292504, A292505, A295279, A300660, A316782.

postfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[postfacs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
oltsfacs[n_]:=If[n<=1,{{}},Prepend[Select[Union@@Function[q,Sort/@Tuples[oltsfacs/@q]]/@DeleteCases[postfacs[n],{n}],UnsameQ@@#&],n]];
Table[Length[oltsfacs[n]],{n,100}]

seq(n)={my(v=vector(n), w=vector(n)); w[1]=v[1]=1; for(k=2, n, w[k]=v[k]+1; forstep(j=n\k*k, k, -k, my(i=j, e=0); while(i%k==0, i/=k; e++; v[j] += binomial(w[k], e)*v[i]))); w} \\ Andrew Howroyd, Nov 18 2018

a(p^n) = A300660(n) for prime p. - Andrew Howroyd, Nov 18 2018

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A067039 The tower function n^{(n-1)!}.

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A316784 Number of orderless identity tree-factorizations of n.

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