A061775 -id:A061775 - cp's OEIS frontend

A358577 Matula-Goebel numbers of "square" rooted trees, i.e., whose height equals their number of leaves.

1, 4, 12, 14, 18, 19, 21, 27, 40, 52, 60, 68, 70, 74, 78, 86, 89, 90, 91, 92, 95, 100, 102, 105, 107, 111, 117, 119, 122, 129, 130, 134, 135, 138, 146, 150, 151, 153, 161, 163, 169, 170, 175, 176, 181, 183, 185, 195, 201, 206, 207, 215, 219, 221, 225, 227, 230

Offset: 1

Gus Wiseman, Nov 25 2022

nonn

The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.

			The terms together with their corresponding rooted trees begin:
   1: o
   4: (oo)
  12: (oo(o))
  14: (o(oo))
  18: (o(o)(o))
  19: ((ooo))
  21: ((o)(oo))
  27: ((o)(o)(o))
  40: (ooo((o)))
  52: (oo(o(o)))
  60: (oo(o)((o)))
  68: (oo((oo)))
  70: (o((o))(oo))
  74: (o(oo(o)))
  78: (o(o)(o(o)))
  86: (o(o(oo)))
  89: ((ooo(o)))
  90: (o(o)(o)((o)))

Gus Wiseman, The first 64 square rooted trees.

Internals instead of leaves: A358576, counted by A358587, ordered A358588.
Internals instead of height: A358578, counted by A185650, ordered A358579.
These trees are counted by A358589, ordered A358590.
A000081 counts rooted trees, ordered A000108.
A034781 counts trees by nodes and height.
A055277 counts trees by nodes and leaves, ordered A001263.
MG statistics: A061775, A109082, A109129, A196050, A342507, A358552.
Cf. A000040, A000720, A001222, A007097, A056239, A112798.
Cf. A206487, A358379, A358580, A358581-A358586, A358592.

MGTree[n_]:=If[n==1,{},MGTree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Count[MGTree[#],{},{0,Infinity}]==Depth[MGTree[#]]-1&]

A358552(a(n)) = A109129(a(n)).

A358552 Node-height of the rooted tree with Matula-Goebel number n. Number of nodes in the longest path from root to leaf.

Original entry on oeis.org

1, 2, 3, 2, 4, 3, 3, 2, 3, 4, 5, 3, 4, 3, 4, 2, 4, 3, 3, 4, 3, 5, 4, 3, 4, 4, 3, 3, 5, 4, 6, 2, 5, 4, 4, 3, 4, 3, 4, 4, 5, 3, 4, 5, 4, 4, 5, 3, 3, 4, 4, 4, 3, 3, 5, 3, 3, 5, 5, 4, 4, 6, 3, 2, 4, 5, 4, 4, 4, 4, 5, 3, 4, 4, 4, 3, 5, 4, 6, 4, 3, 5, 5, 3, 4, 4, 5, 5, 4, 4, 4, 4, 6, 5, 4, 3, 5, 3, 5, 4, 5, 4, 4, 4, 4, 3, 4, 3

Offset: 1

Gus Wiseman, Nov 26 2022

nonn

Edge-height is given by A109082 (see formula).

The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.

			The Matula-Goebel number of ((ooo(o))) is 89, and it has node-height 4, so a(89) = 4.

Antti Karttunen, Table of n, a(n) for n = 1..100000

Positions of first appearances are A007097.
This statistic is counted by A034781, ordered A080936.
The ordered version is A358379(n) + 1.
A000081 counts rooted trees, ordered A000108.
A055277 counts rooted trees by nodes and leaves, ordered A001263.
Other statistics: A061775 (nodes), A109082 (edge-height), A109129 (leaves), A196050 (edges), A342507 (internals).
Cf. A000040, A000720, A001222, A056239, A112798.
Cf. A206487, A358576, A358589, A358592, A358729.

MGTree[n_]:=If[n==1,{},MGTree/@If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
Table[Depth[MGTree[n]]-1,{n,100}]

A358552(n) = { my(v=factor(n)[, 1], d=0); while(#v, d++; v=fold(setunion, apply(p->factor(primepi(p))[, 1]~, v))); (1+d); }; \\ (after Kevin Ryde in A109082) - Antti Karttunen, Oct 23 2023

from functools import lru_cache
from sympy import isprime, primepi, primefactors
@lru_cache(maxsize=None)
def A358552(n):
    if n == 1 : return 1
    if isprime(n): return 1+A358552(primepi(n))
    return max(A358552(p) for p in primefactors(n)) # Chai Wah Wu, Apr 15 2024

a(n) = A109082(n) + 1.

a(n) = A061775(n) - A358729(n). - Antti Karttunen, Oct 23 2023

Data section extended up to a(108) by Antti Karttunen, Oct 23 2023

A091205 Factorization and index-recursion preserving isomorphism from binary codes of GF(2) polynomials to integers.

Original entry on oeis.org

0, 1, 2, 3, 4, 9, 6, 5, 8, 15, 18, 7, 12, 23, 10, 27, 16, 81, 30, 13, 36, 25, 14, 69, 24, 11, 46, 45, 20, 21, 54, 19, 32, 57, 162, 115, 60, 47, 26, 63, 72, 61, 50, 33, 28, 135, 138, 17, 48, 35, 22, 243, 92, 39, 90, 37, 40, 207, 42, 83, 108, 29, 38, 75, 64, 225, 114, 103

Offset: 0

Antti Karttunen, Jan 03 2004

nonn

This "deeply multiplicative" bijection is one of the deep variants of A091203 which satisfy most of the same identities as the latter, but it additionally preserves also the structures where we recurse on irreducible polynomial's A014580-index. E.g., we have: A091238(n) = A061775(a(n)). The reason this holds is that when the permutation is restricted to the binary codes for irreducible polynomials over GF(2) (A014580), it induces itself: a(n) = A049084(a(A014580(n))).

On the other hand, when this permutation is restricted to the union of {1} and reducible polynomials over GF(2) (A091242), permutation A245813 is induced.

Antti Karttunen, Table of n, a(n) for n = 0..8192
A. Karttunen, Scheme-program for computing this sequence.
Index entries for sequences operating on GF(2)[X]-polynomials
Index entries for sequences that are permutations of the natural numbers

Inverse: A091204.
Similar or related permutations: A091203, A106443, A106445, A106447, A235042, A245704, A245813, A245821.
Cf. A000040, A007097, A010051, A014580, A049084, A061775, A091238, A091225, A091226, A091230, A091242.

allocatemem(123456789);
v091226 = vector(2^22);
isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
n=2; while((n < 2^22), if(isA014580(n), v091226[n] = v091226[n-1]+1, v091226[n] = v091226[n-1]); n++)
A091226(n) = v091226[n];
A091205(n) = if(n<=1,n,if(isA014580(n),prime(A091205(A091226(n))),{my(irfs,t); irfs=subst(lift(factor(Mod(1,2)*Pol(binary(n)))),x,2); irfs[,1]=apply(t->A091205(t),irfs[,1]); factorback(irfs)}));
for(n=0, 8192, write("b091205.txt", n, " ", A091205(n)));
\\ Antti Karttunen, Aug 16 2014

a(0)=0, a(1)=1. For n that is coding an irreducible polynomial, that is if n = A014580(i), we have a(n) = A000040(a(i)) and for reducible polynomials a(ir_i X ir_j X ...) = a(ir_i) * a(ir_j) * ..., where ir_i = A014580(i), X stands for carryless multiplication of polynomials over GF(2) (A048720) and * for the ordinary multiplication of integers (A004247).
As a composition of related permutations:
a(n) = A245821(A245704(n)).
Other identities.
For all n >= 0, the following holds:
a(A091230(n)) = A007097(n). [Maps iterates of A014580 to the iterates of primes. Permutation A245704 has the same property.]
For all n >= 1, the following holds:
A010051(a(n)) = A091225(n). [After a(1)=1, maps binary representations of irreducible GF(2) polynomials, A014580, bijectively to primes and the binary representations of corresponding reducible polynomials, A091242, to composite numbers, in some order. The permutations A091203, A106443, A106445, A106447, A235042 and A245704 have the same property.]

Name changed by Antti Karttunen, Aug 16 2014

A324922 a(n) = unique m such that m/A003963(m) = n, where A003963 is product of prime indices.

Original entry on oeis.org

1, 2, 6, 4, 30, 12, 28, 8, 36, 60, 330, 24, 156, 56, 180, 16, 476, 72, 152, 120, 168, 660, 828, 48, 900, 312, 216, 112, 1740, 360, 10230, 32, 1980, 952, 840, 144, 888, 304, 936, 240, 6396, 336, 2408, 1320, 1080, 1656, 8460, 96, 784, 1800, 2856, 624, 848, 432

Offset: 1

Gus Wiseman, Mar 20 2019

Every positive integer has a unique factorization into factors q(i) = prime(i)/i, i > 0 given by the rows of A324924. Then a(n) is the number obtained by encoding this factorization as a standard factorization into prime numbers (A112798).

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Sorting the sequence gives A324850.
Cf. A000081, A003963, A061775, A109129, A112798, A120383, A196050, A317713.
Cf. A324848, A324849, A324923, A324924, A324925, A324931, A324934.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
difac[n_]:=If[n==1,{},With[{m=Product[Prime[i]/i,{i,primeMS[n]}]},Sort[Join[primeMS[n],difac[n/m]]]]];
Table[Times@@Prime/@difac[n],{n,30}]

a(n) = my (f=factor(n)); prod (i=1, #f~, (f[i,1] * a(primepi(f[i,1])))^f[i,2]) \\ Rémy Sigrist, Jul 18 2019

a(n) = Product_t mg(t) where the product is over all (not necessarily distinct) terminal subtrees of the rooted tree with Matula-Goebel number n, and mg(t) is the Matula-Goebel number of t.

Completely multiplicative with a(prime(n)) = prime(n) * a(n). - Rémy Sigrist, Jul 18 2019

Keyword mult added by Rémy Sigrist, Jul 18 2019

A358578 Matula-Goebel numbers of rooted trees whose number of leaves equals their number of internal (non-leaf) nodes.

Original entry on oeis.org

2, 6, 7, 18, 20, 21, 26, 34, 37, 43, 54, 60, 63, 67, 70, 78, 88, 91, 92, 95, 102, 111, 116, 119, 122, 129, 142, 146, 151, 162, 164, 173, 180, 181, 189, 200, 201, 202, 210, 227, 234, 236, 239, 245, 260, 264, 269, 273, 276, 278, 285, 306, 308, 314, 322, 333, 337

Offset: 1

Gus Wiseman, Nov 25 2022

nonn

The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.

			The terms together with their corresponding rooted trees begin:
   2: (o)
   6: (o(o))
   7: ((oo))
  18: (o(o)(o))
  20: (oo((o)))
  21: ((o)(oo))
  26: (o(o(o)))
  34: (o((oo)))
  37: ((oo(o)))
  43: ((o(oo)))
  54: (o(o)(o)(o))
  60: (oo(o)((o)))
  63: ((o)(o)(oo))
  67: (((ooo)))
  70: (o((o))(oo))
  78: (o(o)(o(o)))
  88: (ooo(((o))))
  91: ((oo)(o(o)))

Gus Wiseman, The first 64 rooted trees whose number of leaves equals their number of internal nodes.

These trees are counted by A185650, ordered A358579.
Height instead of leaves: A358576, counted by A358587, ordered A358588.
Height instead of internals: A358577, counted by A358589, ordered A358590.
Positions of 0's in A358580.
A000081 counts rooted trees, ordered A000108.
A034781 counts trees by nodes and height.
A055277 counts trees by nodes and leaves, ordered A001263.
MG statistics: A061775, A109082, A109129, A196050, A342507, A358552.
Cf. A000040, A000720, A001222, A007097, A056239, A112798.
Cf. A206487, A358371, A358581-A358586, A358592.

MGTree[n_]:=If[n==1,{},MGTree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Count[MGTree[#],{},{0,Infinity}]==Count[MGTree[#],[_],{0,Infinity}]&]

A342507(a(n)) = A109129(a(n)).

A331683 One and all numbers of the form 2^k * prime(j) for k > 0 and j already in the sequence.

Original entry on oeis.org

1, 4, 8, 14, 16, 28, 32, 38, 56, 64, 76, 86, 106, 112, 128, 152, 172, 212, 214, 224, 256, 262, 304, 326, 344, 424, 428, 448, 512, 524, 526, 608, 622, 652, 688, 766, 848, 856, 886, 896, 1024, 1048, 1052, 1154, 1216, 1226, 1244, 1304, 1376, 1438, 1532, 1696

Offset: 1

Gus Wiseman, Jan 30 2020

nonn

Also Matula-Goebel numbers of lone-child-avoiding rooted trees at with at most one non-leaf branch under any given vertex. A rooted tree is lone-child-avoiding if there are no unary branchings. The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of the root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.

Also Matula-Goebel numbers of lone-child-avoiding locally disjoint semi-identity trees. Locally disjoint means no branch of any vertex overlaps a different (unequal) branch of the same vertex. In a semi-identity tree, all non-leaf branches of any given vertex are distinct.

			The sequence of all lone-child-avoiding rooted trees with at most one non-leaf branch under any given vertex together with their Matula-Goebel numbers begins:
    1: o
    4: (oo)
    8: (ooo)
   14: (o(oo))
   16: (oooo)
   28: (oo(oo))
   32: (ooooo)
   38: (o(ooo))
   56: (ooo(oo))
   64: (oooooo)
   76: (oo(ooo))
   86: (o(o(oo)))
  106: (o(oooo))
  112: (oooo(oo))
  128: (ooooooo)
  152: (ooo(ooo))
  172: (oo(o(oo)))
  212: (oo(oooo))
  214: (o(oo(oo)))
  224: (ooooo(oo))

Robert Israel, Table of n, a(n) for n = 1..3140

These trees counted by number of vertices are A212804.
The semi-lone-child-avoiding version is A331681.
The non-semi-identity version is A331871.
Lone-child-avoiding rooted trees are counted by A001678.
Matula-Goebel numbers of lone-child-avoiding rooted trees are A291636.
Unlabeled semi-identity trees are counted by A306200, with Matula-Goebel numbers A306202.
Locally disjoint rooted trees are counted by A316473.
Matula-Goebel numbers of locally disjoint rooted trees are A316495.
Lone-child-avoiding locally disjoint rooted trees by leaves are A316697.
Cf. A000081, A007097, A061775, A196050, A276625, A316470, A316696, A331678, A331679, A331680, A331682, A331686, A331687.

N:= 10^4: # for terms <= N
S:= {1}:
with(queue):
Q:= new(1):
while not empty(Q) do
  r:= dequeue(Q);
  p:= ithprime(r);
  newS:= {seq(2^i*p,i=1..ilog2(N/p))} minus S;
  S:= S union newS;
  for s in newS do enqueue(Q,s) od:
od:
sort(convert(S,list)); # Robert Israel, Feb 05 2020

uryQ[n_]:=n==1||MatchQ[FactorInteger[n],({{2,},{p,1}}/;uryQ[PrimePi[p]])|({{2,k_}}/;k>1)];
Select[Range[100],uryQ]

Intersection of A291636, A316495, and A306202.

A358576 Matula-Goebel numbers of rooted trees whose node-height equals their number of internal (non-leaf) nodes.

Original entry on oeis.org

9, 15, 18, 21, 23, 30, 33, 35, 36, 39, 42, 46, 47, 49, 51, 57, 60, 61, 66, 70, 72, 73, 77, 78, 83, 84, 87, 91, 92, 93, 94, 95, 98, 102, 111, 113, 114, 119, 120, 122, 123, 129, 132, 133, 137, 140, 144, 146, 149, 151, 154, 156, 159, 166, 167, 168, 174, 177, 181

Offset: 1

Gus Wiseman, Nov 25 2022

nonn

The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.

Node-height is the number of nodes in the longest path from root to leaf.

			The terms together with their corresponding rooted trees begin:
   9: ((o)(o))
  15: ((o)((o)))
  18: (o(o)(o))
  21: ((o)(oo))
  23: (((o)(o)))
  30: (o(o)((o)))
  33: ((o)(((o))))
  35: (((o))(oo))
  36: (oo(o)(o))
  39: ((o)(o(o)))
  42: (o(o)(oo))
  46: (o((o)(o)))
  47: (((o)((o))))
  49: ((oo)(oo))
  51: ((o)((oo)))
  57: ((o)(ooo))
  60: (oo(o)((o)))
  61: ((o(o)(o)))

Gus Wiseman, The first 64 rooted trees whose node-height equals their number of internal nodes.

The version for edge-height is A209638.
Square trees are A358577, counted by A358589, ordered A358590.
The version for leaves instead of height is A358578, counted by A185650.
These trees are counted by A358587, ordered A358588.
A000081 counts rooted trees, ordered A000108.
A034781 counts rooted trees by nodes and height.
A055277 counts rooted trees by leaves, ordered A001263.
MG statistics: A061775, A109082, A109129, A196050, A342507, A358552.
Cf. A000040, A000720, A001222, A007097, A056239, A112798.
Cf. A206487, A358580, A358581-A358586, A358592, A358729.

MGTree[n_]:=If[n==1,{},MGTree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Count[MGTree[#],[_],{0,Infinity}]==Depth[MGTree[#]]-1&]

A358552(a(n)) = A342507(a(n)).

A358580 Difference between the number of leaves and the number of internal (non-leaf) nodes in the rooted tree with Matula-Goebel number n.

Original entry on oeis.org

1, 0, -1, 1, -2, 0, 0, 2, -1, -1, -3, 1, -1, 1, -2, 3, -1, 0, 1, 0, 0, -2, -2, 2, -3, 0, -1, 2, -2, -1, -4, 4, -3, 0, -1, 1, 0, 2, -1, 1, -2, 1, 0, -1, -2, -1, -3, 3, 1, -2, -1, 1, 2, 0, -4, 3, 1, -1, -2, 0, -1, -3, 0, 5, -2, -2, 0, 1, -2, 0, -1, 2, -1, 1, -3

Offset: 1

Gus Wiseman, Nov 25 2022

sign

The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.

			The Matula-Goebel number of ((ooo(o))) is 89, and it has 4 leaves and 3 internal nodes, so a(89) = 1.

Zeros are A358578, counted by A185650 (ordered A358579).
Positions of positive terms are counted by A358581, negative A358582.
Positions of nonnegative terms are counted by A358583, nonpositive A358584.
A000081 counts rooted trees, ordered A000108.
A034781 counts trees by nodes and height.
A055277 counts trees by nodes and leaves, ordered A001263.
MG statistics: A061775, A109082, A109129, A196050, A342507, A358552.
Cf. A000040, A000720, A001222, A007097, A056239, A112798.
Cf. A206487, A358371, A358576, A358577, A358592.

MGTree[n_]:=If[n==1,{},MGTree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Count[MGTree[n],{},{0,Infinity}]-Count[MGTree[n],[_],{0,Infinity}],{n,100}]

a(n) = A109129(n) - A342507(n).

A317710 Uniform tree numbers. Matula-Goebel numbers of uniform rooted trees.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 62, 64, 65, 66, 67, 69, 70, 73, 77, 78, 79, 81, 82, 83, 85, 86, 87, 91, 93, 94, 95, 97

Offset: 1

Gus Wiseman, Aug 05 2018

nonn

A positive integer n is a uniform tree number iff either n = 1 or n is a power of a squarefree number whose prime indices are also uniform tree numbers. A prime index of n is a number m such that prime(m) divides n.

A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp.1-12.

Cf. A061775, A072774, A111299, A214577, A276625, A277098, A303431, A317589.

Cf. A317705, A317707, A317708, A317709, A317711 (complement), A317712, A317717, A317718.

rupQ[n_]:=Or[n==1,And[SameQ@@FactorInteger[n][[All,2]],And@@rupQ/@PrimePi/@FactorInteger[n][[All,1]]]];
Select[Range[100],rupQ]

A358372 Number of nodes in the n-th standard ordered rooted tree.

Original entry on oeis.org

1, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 5, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8

Offset: 1

Gus Wiseman, Nov 14 2022

nonn

We define the n-th standard ordered rooted tree to be obtained by taking the (n-1)-th composition in standard order (graded reverse-lexicographic, A066099) as root and replacing each part with its own standard ordered rooted tree. This ranking is an ordered variation of Matula-Goebel numbers, giving a bijective correspondence between positive integers and unlabeled ordered rooted trees.

			The standard ordered rooted tree ranking begins:
  1: o        10: (((o))o)   19: (((o))(o))
  2: (o)      11: ((o)(o))   20: (((o))oo)
  3: ((o))    12: ((o)oo)    21: ((o)((o)))
  4: (oo)     13: (o((o)))   22: ((o)(o)o)
  5: (((o)))  14: (o(o)o)    23: ((o)o(o))
  6: ((o)o)   15: (oo(o))    24: ((o)ooo)
  7: (o(o))   16: (oooo)     25: (o(oo))
  8: (ooo)    17: ((((o))))  26: (o((o))o)
  9: ((oo))   18: ((oo)o)    27: (o(o)(o))
For example, the 25th ordered tree is (o,(o,o)) because the 24th composition is (1,4) and the 3rd composition is (1,1). Hence a(25) = 5.

Gus Wiseman, Statistics, classes, and transformations of standard compositions

The triangle counting trees by leaves is A001263, unordered A055277.
The version for unordered trees is A061775, leaves A109129, edges A196050.
The leaves are counted by A358371.
A000081 counts unlabeled rooted trees, ranked by A358378.
A358374 ranks ordered identity trees, counted by A032027.
A358375 ranks ordered binary trees, counted by A126120
Cf. A001678, A004249, A005043, A063895, A284778, A358373, A358376, A358377.

stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
srt[n_]:=If[n==1,{},srt/@stc[n-1]];
Table[Count[srt[n],_,{0,Infinity}],{n,100}]

cp's OEIS Frontend

A358577 Matula-Goebel numbers of "square" rooted trees, i.e., whose height equals their number of leaves.

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A358552 Node-height of the rooted tree with Matula-Goebel number n. Number of nodes in the longest path from root to leaf.

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A091205 Factorization and index-recursion preserving isomorphism from binary codes of GF(2) polynomials to integers.

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A324922 a(n) = unique m such that m/A003963(m) = n, where A003963 is product of prime indices.

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A358578 Matula-Goebel numbers of rooted trees whose number of leaves equals their number of internal (non-leaf) nodes.

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A331683 One and all numbers of the form 2^k * prime(j) for k > 0 and j already in the sequence.

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Maple

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A358576 Matula-Goebel numbers of rooted trees whose node-height equals their number of internal (non-leaf) nodes.

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