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

22, 26, 33, 34, 38, 39, 44, 46, 51, 52, 55, 57, 58, 62, 65, 66, 68, 69, 74, 76, 77, 78, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 99, 102, 104, 106, 110, 111, 114, 115, 116, 117, 118, 119, 122, 123, 124, 129, 130, 132, 133, 134, 136, 138, 141, 142, 145, 146

Offset: 1

Author

Reinhard Zumkeller, Jul 13 2003

Keywords

• nonn

Comments

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

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Diagram showing numbers k in this sequence 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.
• Eric Weisstein's World of Mathematics, Smooth Number.

Crossrefs

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

Programs

Mathematica

okQ[n_] := AnyTrue[{2, 3, 5, 7}, Divisible[n, #]&] && FactorInteger[n][[-1, 1]] > 7;
Select[Range[1000], okQ] (* Jean-François Alcover, Oct 15 2021 *)

PARI

mult2357(m,n) = \\ mult 2,3,5,7 not 7 smooth
{
local(x,a,j,f,ln);
for(x=m,n,
f=0;
if(gcd(x,210)>1,
a = ifactor(x);
for(j=1,length(a),
if(a[j]>7,f=1;break);
);
if(f,print1(x","));
);
);
}
ifactor(n) = \\ The vector of the prime factors of n with multiplicity.
{
local(f,j,k,flist);
flist=[];
f=Vec(factor(n));
for(j=1,length(f[1]),
for(k = 1,f[2][j],flist = concat(flist,f[1][j])
);
);
return(flist)
}
\\ Cino Hilliard, Jul 03 2009

Python

from sympy import primefactors
def ok(n):
    pf = set(primefactors(n))
    return pf & {2, 3, 5, 7} and pf - {2, 3, 5, 7}
print(list(filter(ok, range(147)))) # Michael S. Branicky, Oct 15 2021