A084891 - OEIS

%I #22 Apr 04 2023 10:33:46

%S 22,26,33,34,38,39,44,46,51,52,55,57,58,62,65,66,68,69,74,76,77,78,82,

%T 85,86,87,88,91,92,93,94,95,99,102,104,106,110,111,114,115,116,117,

%U 118,119,122,123,124,129,130,132,133,134,136,138,141,142,145,146

%N Multiples of 2, 3, 5, or 7, but not 7-smooth.

%C Intersection of A068191 with (A005843, A008585, A008587 and A008589); union of (A005843, A008585, A008587 and A008589) without A002473.

%C A020639(a(n)) <= 7, A006530(a(n)) > 7.

%H Michael De Vlieger, <a href="/A084891/b084891.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael De Vlieger, <a href="/A084891/a084891.png">Diagram showing numbers k in this sequence</a> instead as k mod 210, in black, else white if k is coprime to 210, purple if k = 1, red if k | 210, and gold if rad(k) | 210, magnification 5X.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmoothNumber.html">Smooth Number</a>.

%t okQ[n_] := AnyTrue[{2, 3, 5, 7}, Divisible[n, #]&] && FactorInteger[n][[-1, 1]] > 7;

%t Select[Range[1000], okQ] (* _Jean-François Alcover_, Oct 15 2021 *)

%o (PARI) mult2357(m,n) = \\ mult 2,3,5,7 not 7 smooth

%o {

%o local(x,a,j,f,ln);

%o for(x=m,n,

%o f=0;

%o if(gcd(x,210)>1,

%o a = ifactor(x);

%o for(j=1,length(a),

%o if(a[j]>7,f=1;break);

%o );

%o if(f,print1(x","));

%o );

%o );

%o }

%o ifactor(n) = \\ The vector of the prime factors of n with multiplicity.

%o {

%o local(f,j,k,flist);

%o flist=[];

%o f=Vec(factor(n));

%o for(j=1,length(f[1]),

%o for(k = 1,f[2][j],flist = concat(flist,f[1][j])

%o );

%o );

%o return(flist)

%o }

%o \\ _Cino Hilliard_, Jul 03 2009

%o (Python)

%o from sympy import primefactors

%o def ok(n):

%o     pf = set(primefactors(n))

%o     return pf & {2, 3, 5, 7} and pf - {2, 3, 5, 7}

%o print(list(filter(ok, range(147)))) # _Michael S. Branicky_, Oct 15 2021

%Y Cf. A002473, A005843, A006530, A008585, A008587, A008589, A020639, A068191, A080672.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 13 2003