A038564 -id:A038564 - cp's OEIS frontend

A045816 Number of times the digits are repeated in A045815.

1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 8, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6

Offset: 1

Naohiro Nomoto

			Divisors of 20345 are (1,20345), the numbers of digits are [0(1),1(1),2(1),3(1),4(1),5(1)], so a(1) = 1.
Divisors of 45050 are (1,2,3,10,4505,13414,22323,45050), the numbers of digits (0-5) are [0(4),1(4),2(4),3(4),4(4),5(4)], so a(10) = 4.

Naohiro Nomoto, In the list of divisors of n,...

Cf. A038564, A038565.

isA045816 := proc(n) local c,j,b,h,a ; a := [0,0,0,0,0,0] : c := numtheory[divisors](n): for j from 1 to nops(c) do b := convert(c[j], base, 6); for h from 1 to nops(b) do a[b[h]+1] := a[b[h]+1]+1: end do: end do: if(a[1]=a[2] and a[2]=a[3] and a[3]=a[4] and a[4]=a[5] and a[5]=a[6]) then a[1] ; else -1 ; end if: end: n := 1: while true do a := isA045816(n) : if a >= 0 then printf("%d, ",a) ; fi ; n := n+1 : od : # R. J. Mathar, Jun 26 2007

More terms from Sean A. Irvine, Sep 26 2011

A045869 Integers k such that in the list of divisors of k (in base 5), each digit 0-4 appears equally often.

Original entry on oeis.org

2034, 2403, 2430, 3024, 3042, 3240, 3304, 3340, 3420, 4203, 4230, 4302, 4320, 4330, 4340, 213330, 303240, 310430, 330101, 1230134, 1240404, 1303034, 1322340, 1330304, 1340303, 1343030, 2000434, 2004120, 2244030, 2420401, 3020002

Offset: 1

Naohiro Nomoto

Naohiro Nomoto, In the list of divisors of n,...

Cf. A038564, A038565.

A045870 Number of times the digits are repeated in A045869.

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 2, 4, 2, 2, 2, 1, 6, 4, 4, 8, 8, 8, 4, 3, 6, 3, 12, 3, 3, 6, 6, 12, 12, 6, 6, 10, 10, 10, 5, 10, 5, 5, 20, 5, 10, 7, 14, 28, 22, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 22, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2

Offset: 0

Naohiro Nomoto

			A045869(1) = 2034, and the divisors of 2034_5 = 269 (a prime) are 1 and 269; in base 5, these are 1 and 2034. Each digit from 0 through 4 appears exactly once, so a(1) = 1.
A045869(2) = 2403; 2403_5 = 353 (a prime) has divisors 1 and 353, which in base 5 are 1 and 2403, so each digit in 0..4 appears exactly once, so a(2) = 2.
A045869(3) = 2430; 2430_5 = 365 = 5*73, so its divisors are 1, 5, 73, and 365, which in base 5 are 1, 10, 243, and 2430, so each digit in 0..4 appears exactly twice, so a(3) = 2.

Naohiro Nomoto, In the list of divisors of n, ...

Cf. A038564, A038565, A045869.

Examples edited by Jon E. Schoenfield, Nov 12 2022

A045871 Numbers n with the property that in the list of divisors of n (in octal), each digit 0-7 appears equally often.

Original entry on oeis.org

2035467, 2037465, 2046375, 2046573, 2047365, 2047563, 2056743, 2057643, 2063457, 2063475, 2067345, 2074365, 2074635, 2075463, 2076345, 2076453, 2307645, 2347065, 2356047, 2360547, 2364075, 2365407, 2406537, 2407365, 2407653, 2430675, 2436075

Offset: 1

Naohiro Nomoto

			Divisors of 2035467 are (1,2035467); the numbers of digits (0-7) are [ 0(1),1(1),2(1),3(1),4(1),5(1),6(1),7(1) ].

N. Nomoto, In the list of divisors of n,...

Cf. A038564, A038565.

Missing terms inserted by Sean A. Irvine, Mar 22 2021

A273094 a(n) is the smallest number whose divisors contain each 0..9 digit exactly n times.

Original entry on oeis.org

203457869, 206893558, 507083396, 506815954, 102668478970, 895233580, 26475394180, 887692930, 10708845258, 13306408052, 155503137452, 963213572, 803503960576, 40349550036, 203264657940

Offset: 1

Giovanni Resta, May 15 2016

We also have a(18)=18174907880, a(19)=81418065258, a(20)=257678968520, and a(23)=529539876740. The missing terms are all greater than 10^12.

			a(1)=203457869, whose divisors are 1 and 203457869 itself. a(2)=206893558, whose divisors, i.e., 1, 2, 103446779, and 206893558, contain each digit 2 times.

Cf. A038564, A059436, A243363.

cp's OEIS Frontend

A045816 Number of times the digits are repeated in A045815.

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A045869 Integers k such that in the list of divisors of k (in base 5), each digit 0-4 appears equally often.

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A045870 Number of times the digits are repeated in A045869.

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A045871 Numbers n with the property that in the list of divisors of n (in octal), each digit 0-7 appears equally often.

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A273094 a(n) is the smallest number whose divisors contain each 0..9 digit exactly n times.

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