A086557 Smallest number not included earlier, beginning with 2 and having prime signature of n.

2, 23, 25, 29, 21, 211, 27, 289, 22, 223, 20, 227, 26, 201, 2401, 229, 28, 233, 207, 202, 203, 239, 24, 2209, 205, 2197, 212, 241, 222, 251, 243, 206, 209, 213, 225, 257, 214, 215, 232, 263, 230, 269, 236, 242, 217, 271, 208, 2809, 244, 218, 245, 277, 248, 219

Offset

2,1

Comments

A rearrangement of numbers beginning with 2.

Links

Robert Israel, Table of n, a(n) for n = 2..2000

Example

a(40) = 232 = 2^3 * 29 as 40 = 2^3 * 5.

Maple

se := {seq(20+k, k=0..9), seq(200+k, k=0..99), seq(2000+k, k=0..999), seq(20000+k, k=0..9999), seq(200000+k, k=0..99999)}: a[2] := 2:for n from 3 to 60 do l := sort(convert(se, list)): ifa := ifactors(n):no := nops(ifa[2]): prisig := sort([seq(ifa[2][j][2], j=1..no)]):h := 0:while(true) do h := h+1: ifa := ifactors(l[h]): no2 := nops(ifa[2]):prisig2 := sort([seq(ifa[2][j][2], j=1..no2)]):ok := true: if(no<>no2) then ok := false: else for w from 1 to no do if(prisig[w]<>prisig2[w]) then ok := false:break:fi:od:fi: if(ok=true) then a[n] := l[h]:se := se minus {l[h]}:break:fi:od:od:seq(a[q], q=2..60); # Sascha Kurz
# alternative
ps:= proc(n) local t; sort(map(t -> t[2], ifactors(n)[2])) end proc:
R:= NULL: PS:= 'PS':
with(queue):
PS[[6]]:= new(17^6, 37^6): PS[[5]]:= new(3^5, 19^5): PS[[9]]:= new(11^9, 31^9 ):
PS[[10]]:= new(7^10):
d:= 0: x:= 1:
for n from 2 to 1000 while x < 10^7 do
  X:= ps(n);
  if not assigned(PS[X]) then PS[X]:= new() fi;
  flag:= empty(PS[X]);
  while flag do
    x:= x+1;
    if x >= 3*10^d then d:= d+1; x:= 2*10^d fi;
    Y:= ps(x);
    if not assigned(PS[Y]) then PS[Y]:= new() fi;
    if empty(PS[Y]) or x > front(PS[Y]) then enqueue(PS[Y], x) fi;
    flag:= (Y<>X);
  od;
  y:= dequeue(PS[X]);
  R:= R, y;
od:
R; # Robert Israel, Apr 19 2021

Mathematica

Block[{a = {}, s = PositionIndex@ Table[ToString@ Sort[FactorInteger[n][[All, -1]]], {n, Product[Prime@ i, {i, 6}]}]}, Do[AppendTo[a, #] &@ SelectFirst[Lookup[s, ToString@ Sort[FactorInteger[n][[All, -1]]] ], And[First@ IntegerDigits@ # == 2, FreeQ[a, #]] &], {n, 2, 55}]; a] (* Michael De Vlieger, Aug 15 2017 *)

Crossrefs

Cf. A086549.

Sequence in context: A131983 A153718 A105813 * A042797 A041649 A141533

Adjacent sequences: A086554 A086555 A086556 * A086558 A086559 A086560

Keyword

base,nonn

Author

Amarnath Murthy, Aug 30 2003

Extensions

Corrected and extended by Sascha Kurz, Sep 22 2003

Status

approved