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A084891 Multiples of 2, 3, 5, or 7, but not 7-smooth.

%I A084891 #23 Feb 16 2025 08:32:49
%S A084891 22,26,33,34,38,39,44,46,51,52,55,57,58,62,65,66,68,69,74,76,77,78,82,
%T A084891 85,86,87,88,91,92,93,94,95,99,102,104,106,110,111,114,115,116,117,
%U A084891 118,119,122,123,124,129,130,132,133,134,136,138,141,142,145,146
%N A084891 Multiples of 2, 3, 5, or 7, but not 7-smooth.
%C A084891 Intersection of A068191 with (A005843, A008585, A008587 and A008589); union of (A005843, A008585, A008587 and A008589) without A002473.
%C A084891 A020639(a(n)) <= 7, A006530(a(n)) > 7.
%H A084891 Michael De Vlieger, <a href="/A084891/b084891.txt">Table of n, a(n) for n = 1..10000</a>
%H A084891 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 A084891 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmoothNumber.html">Smooth Number</a>.
%t A084891 okQ[n_] := AnyTrue[{2, 3, 5, 7}, Divisible[n, #]&] && FactorInteger[n][[-1, 1]] > 7;
%t A084891 Select[Range[1000], okQ] (* _Jean-François Alcover_, Oct 15 2021 *)
%o A084891 (PARI) mult2357(m,n) = \\ mult 2,3,5,7 not 7 smooth
%o A084891 {
%o A084891 local(x,a,j,f,ln);
%o A084891 for(x=m,n,
%o A084891 f=0;
%o A084891 if(gcd(x,210)>1,
%o A084891 a = ifactor(x);
%o A084891 for(j=1,length(a),
%o A084891 if(a[j]>7,f=1;break);
%o A084891 );
%o A084891 if(f,print1(x","));
%o A084891 );
%o A084891 );
%o A084891 }
%o A084891 ifactor(n) = \\ The vector of the prime factors of n with multiplicity.
%o A084891 {
%o A084891 local(f,j,k,flist);
%o A084891 flist=[];
%o A084891 f=Vec(factor(n));
%o A084891 for(j=1,length(f[1]),
%o A084891 for(k = 1,f[2][j],flist = concat(flist,f[1][j])
%o A084891 );
%o A084891 );
%o A084891 return(flist)
%o A084891 }
%o A084891 \\ _Cino Hilliard_, Jul 03 2009
%o A084891 (Python)
%o A084891 from sympy import primefactors
%o A084891 def ok(n):
%o A084891     pf = set(primefactors(n))
%o A084891     return pf & {2, 3, 5, 7} and pf - {2, 3, 5, 7}
%o A084891 print(list(filter(ok, range(147)))) # _Michael S. Branicky_, Oct 15 2021
%Y A084891 Cf. A002473, A005843, A006530, A008585, A008587, A008589, A020639, A068191, A080672.
%K A084891 nonn
%O A084891 1,1
%A A084891 _Reinhard Zumkeller_, Jul 13 2003