A106600 - OEIS

%I #13 Nov 14 2019 12:19:52

%S 1,10,46,141,338,694,1273,2155,3427,5194,7575,10688,14672,19674,25861,

%T 33406,42487,53302,66061,80988,98311,118271,141124,167139,196597,

%U 229785,267007,308575,354820,406074,462692,525030,593467,668384,750177,839260

%N Number of positive integers <= 10^n that are divisible by no prime exceeding 7.

%C Position of 10^n among the 7-smooth numbers (A002473). Note that all powers of 10 are in A002473. - _Zak Seidov_, Nov 18 2013

%H Zak Seidov, <a href="/A106600/b106600.txt">Table of n, a(n) for n = 0..200</a>

%e A002473(a(2)) = A002473(46)=100.

%t n = 35; t = Select[ Flatten[ Table[ 7^d*Select[ Flatten[ Table[ 5^c*Select[ Flatten[ Table[2^a*3^b, {a, 0, n*Log[2, 10]}, {b, 0, n*Log[3, 10]}]], # <= 10^n &], {c, 0, n*Log[5, 10]}]], # <= 10^n &], {d, 0, n*Log[5, 10]}]], # <= 10^n &]; Table[ Length[ Select[t, # <= 10^n &]], {n, 0, 35}]

%Y Row 4 of A253635.

%Y Cf. A002473, A011557.

%K nonn

%O 0,2

%A _Robert G. Wilson v_, May 27 2005