A108276 Number of positive integers <= 10^n that are divisible by no prime exceeding 19.

1, 10, 72, 331, 1169, 3419, 8751, 20198, 42950, 85411, 160626, 288126, 496303, 825326, 1330766, 2088013, 3197529, 4791093, 7039193, 10159603, 14427309, 20186026, 27861175, 37974797, 51162295, 68191379, 89983125, 117635672

Offset: 0

Author

Robert G. Wilson v, May 31 2005

Keywords

• nonn

Crossrefs

Row 8 of A253635.

Cf. A123384, A100752, A106598, A106600, A107352, A106629, A108275, A108277, A011557, A080682.

Programs

Mathematica

n = 9; t = Select[ Flatten[ Table[19^h*Select[ Flatten[ Table[17^g*Select[ Flatten[ Table[13^f*Select[ Flatten[ Table[11^e*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[7, 10]}]], # <= 10^n &], {e, 0, n*Log[11, 10]}]], # <= 10^n &], {f, 0, n*Log[13, 10]}]], # <= 10^n &], {g, 0, n*Log[17, 10]}]], # <= 10^n &], {h, 0, n*Log[19, 10]}]], # <= 10^n &]; Table[ Length[ Select[t, # <= 10^n &]], {n, 0, 10}]

Extensions

a(10)-a(18) from Donovan Johnson, Sep 16 2009

a(19)-a(27) from Max Alekseyev, Apr 28 2010