A069105 -id:A069105 - cp's OEIS frontend

A132740 Largest divisor of n coprime to 10.

1, 1, 3, 1, 1, 3, 7, 1, 9, 1, 11, 3, 13, 7, 3, 1, 17, 9, 19, 1, 21, 11, 23, 3, 1, 13, 27, 7, 29, 3, 31, 1, 33, 17, 7, 9, 37, 19, 39, 1, 41, 21, 43, 11, 9, 23, 47, 3, 49, 1, 51, 13, 53, 27, 11, 7, 57, 29, 59, 3, 61, 31, 63, 1, 13, 33, 67, 17, 69, 7, 71, 9, 73, 37, 3, 19, 77, 39, 79, 1, 81

Offset: 1

Reinhard Zumkeller, Aug 27 2007

Or: n with all factors of 2 and 5 removed. - M. F. Hasler, Apr 25 2017

			a(1050) = a(2*3*5*5*7) = 3*7 = 21.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000265, A003592, A069105, A070021, A070022, A070023, A132739, A132741.

a132740 = a132739 . a000265  -- Reinhard Zumkeller, Apr 08 2011

A132740 := proc(n) n/A132741(n) ; end proc: # R. J. Mathar, Sep 06 2011

a[n_] := FixedPoint[ Quotient[#, GCD[#, 10]]& , n]; Table[a[n], {n, 1, 81}] (* Jean-François Alcover, Sep 06 2011, after Vladimir Joseph Stephan Orlovsky *)
Table[SelectFirst[Reverse[Divisors[n]],CoprimeQ[#,10]&],{n,90}] (* Uses the SelectFirst function from Mathematica version 10. - Harvey P. Dale, Mar 22 2015 *)
a[n_] := n / Times @@ ({2, 5}^IntegerExponent[n, {2, 5}]); Array[a, 100] (* Amiram Eldar, Jun 12 2022 *)

a(n)=n/5^valuation(n,5)>>valuation(n,2) \\ Charles R Greathouse IV, Sep 06 2011

a(n) = A000265(A132739(n)) = A132739(A000265(n)) = n / A132741(n);
A051626(a(n)) = A051626(n); A007732(a(n)) = A007732(n);
a(A003592(n)) = 1.
Multiplicative with a(2^e) = 1, a(5^e) = 1 and a(p^e) = p^e for p = 3 and p >= 7.
Dirichlet g.f. zeta(s-1)*(2^s-2)*(5^s-5)/((2^s-1)*(5^s-1)). - R. J. Mathar, Sep 06 2011
Sum_{k=1..n} a(k) ~ (5/18) * n^2. - Amiram Eldar, Nov 28 2022

Edited by M. F. Hasler, Apr 25 2017

A070021 1/n has period 1 in base 10 (but not terminating).

Original entry on oeis.org

3, 6, 9, 12, 15, 18, 24, 30, 36, 45, 48, 60, 72, 75, 90, 96, 120, 144, 150, 180, 192, 225, 240, 288, 300, 360, 375, 384, 450, 480, 576, 600, 720, 750, 768, 900, 960, 1125, 1152, 1200, 1440, 1500, 1536, 1800, 1875, 1920, 2250, 2304, 2400, 2880, 3000, 3072, 3600

Offset: 1

Henry Bottomley, Apr 12 2002

			12 is in the sequence since 1/12=0.08333333333...; 11 is not since 1/11=0.0909090909...; 10 is not, since despite 1/10=0.099999999..., it is also true that 1/10=0.1 exactly.

Michael De Vlieger, Table of n, a(n) for n = 1..11778 (a(n) < 10^50)

Cf. A003592, A069105, A070022, A070023.

mx = 5000; Select[ Union@ Flatten@ Table[2^t*5^f {3, 9}, {t, 0, Log[2, mx/3]}, {f, 0, Log[5, mx/(2^t*3)]}], # < mx &] (* Robert G. Wilson v, Apr 27 2017 *)

Numbers of the form a*b*c where a is in {3, 9}, b is a power of 2 and c is a power of 5.

A070023 1/n has period 1 in base 10 (including terminating decimals).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 125, 128, 144, 150, 160, 180, 192, 200, 225, 240, 250, 256, 288, 300, 320, 360, 375, 384, 400, 450, 480, 500, 512, 576, 600, 625, 640, 720, 750

Offset: 1

Henry Bottomley, Apr 12 2002

			12 is in the sequence since 1/12 = 0.08333333333...
11 is not since 1/11 = 0.0909090909...
10 is in, since 1/10 = 0.1000000... = 0.099999999...

Cf. A003592, A069105, A070021, A070022.

Select[Range[750], Length[RealDigits[1/#][[1, -1]]] <= 1 &] (* Amiram Eldar, Jun 12 2022 *)

a(n) = A070022(n)/11. Numbers of the form a*b*c where a is in {1, 3, 9}, b is a power of 2 and c is a power of 5.

A070022 1/n has period 2 in base 10.

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 88, 99, 110, 132, 165, 176, 198, 220, 264, 275, 330, 352, 396, 440, 495, 528, 550, 660, 704, 792, 825, 880, 990, 1056, 1100, 1320, 1375, 1408, 1584, 1650, 1760, 1980, 2112, 2200, 2475, 2640, 2750, 2816, 3168, 3300, 3520, 3960, 4125

Offset: 1

Henry Bottomley, Apr 12 2002

			176 is in the sequence since 1/176=0.00568181818181818...

Cf. A018282, A003592, A069105, A070021, A070023.

Select[Range[5000],Length[RealDigits[1/#][[1,-1]]]==2&] (* Harvey P. Dale, Oct 10 2011 *)

a(n) =11*A070023(n). Numbers of the form a*b*c where a is in {11, 33, 99}, b is a power of 2 and c is a power of 5.

A069858 1/n has period 4 in base 10.

Original entry on oeis.org

101, 202, 303, 404, 505, 606, 808, 909, 1010, 1111, 1212, 1515, 1616, 1818, 2020, 2222, 2424, 2525, 3030, 3232, 3333, 3636, 4040, 4444, 4545, 4848, 5050, 5555, 6060, 6464, 6666, 7272, 7575, 8080, 8888, 9090, 9696, 9999, 10100, 11110, 12120, 12625

Offset: 1

Henry Bottomley, May 02 2002

			1212 is in the sequence since 1/1212=0.0008250825082508250825082508250....

Cf. A027894, A003592, A069105, A070021, A070022, A070023.

Select[Range[13000],Length[RealDigits[1/#][[1,-1]]]==4&] (* Harvey P. Dale, Jun 30 2017 *)

Numbers of the form a*b*c where a is in {101, 303, 909, 1111, 3333, 9999}, b is a power of 2 and c is a power of 5.

cp's OEIS Frontend

A132740 Largest divisor of n coprime to 10.

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A070021 1/n has period 1 in base 10 (but not terminating).

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A070023 1/n has period 1 in base 10 (including terminating decimals).

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A070022 1/n has period 2 in base 10.

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A069858 1/n has period 4 in base 10.

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