A080195 11-smooth numbers which are not 7-smooth.

11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 154, 165, 176, 198, 220, 231, 242, 264, 275, 297, 308, 330, 352, 363, 385, 396, 440, 462, 484, 495, 528, 539, 550, 594, 605, 616, 660, 693, 704, 726, 770, 792, 825, 847, 880, 891, 924, 968, 990, 1056, 1078, 1089

Offset

1,1

Comments

Numbers of the form 2^r*3^s*5^t*7^u*11^v with r, s, t, u >= 0, v > 0.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = 11 * A051038(n). - David A. Corneth, May 27 2017

Sum_{n>=1} 1/a(n) = 7/16. - Amiram Eldar, Nov 10 2020

Example

33 = 3*11 is a term but 35 = 5*7 is not.

Maple

N:= 10^6; # to get all terms <= N
A:= NULL;
for v from 1 to floor(log[11](N)) do
   V:= 11^v;
   for u from 0 to floor(log[7](N/V)) do
      U:= 7^u*V;
      for t from 0 to floor(log[5](N/U)) do
        T:= 5^t*U;
        for s from 0 to floor(log[3](N/T)) do
          S:= 3^s*T;
          for r from 0 to floor(log[2](N/S)) do
             A:= A, 2^r*S
          od
         od
       od
    od
od:
{A}; # Robert Israel, May 28 2014

Mathematica

Select[Range[1000], FactorInteger[#][[-1, 1]] == 11 &] (* Amiram Eldar, Nov 10 2020 *)

Prog

(PARI) {m=1100; z=[]; for(r=0, floor(log(m)/log(2)), a=2^r; for(s=0, floor(log(m/a)/log(3)), b=a*3^s; for(t=0, floor(log(m/b)/log(5)), c=b*5^t; for(u=0, floor(log(m/c)/log(7)), d=c*7^u; for(v=1, floor(log(m/d)/log(11)), z=concat(z, d*11^v)))))); z=vecsort(z); for(i=1, length(z), print1(z[i], ", "))}

Crossrefs

Cf. A051038, A002473.

Sequence in context: A059632 A008593 A135499 * A004920 A136613 A352535

Adjacent sequences: A080192 A080193 A080194 * A080196 A080197 A080198

Keyword

easy,nonn

Author

Klaus Brockhaus, Feb 10 2003

Status

approved