A283611 -id:A283611 - cp's OEIS frontend

A083895 Number of divisors of n with largest digit = 8 (base 10).

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 1, 2, 1, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset: 1

Reinhard Zumkeller, May 08 2003

			n=72, 2 of the 12 divisors of 72 have largest digit =8: {8,18}, therefore a(72)=2.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A054055, A000005, A083903, A083888, A083889, A083890, A083891, A083892, A083893, A083894, A083896, A283611.

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 8:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

With[{k = 8}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1 ;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (* Michael De Vlieger, Oct 06 2019 *)

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083891(n) - A083892(n) - A083893(n) - A083894(n) - A083896(n) = A083903(n) - A083902(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283611(k) = 11.62909500243165896645... . - Amiram Eldar, Jan 04 2024

A283608 Numbers whose largest decimal digit is 5.

Original entry on oeis.org

5, 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 105, 115, 125, 135, 145, 150, 151, 152, 153, 154, 155, 205, 215, 225, 235, 245, 250, 251, 252, 253, 254, 255, 305, 315, 325, 335, 345, 350, 351, 352, 353, 354, 355, 405, 415, 425, 435, 445, 450, 451, 452, 453, 454

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 5.
Number of terms less than 10^n is 6^n - 5^n.
Subsequence of A011535. - David A. Corneth, Mar 25 2017
Prime terms are in A106097.

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Cf. A011535, A054055, A106097.

Cf. Sequences of numbers whose largest decimal digit is k (for k = 1..9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), this sequence (k = 5), A283609 (k = 6), A283610 (k = 7), A283611 (k = 8), A011539 (k = 9).

Filtered([1..500],n->Maximum(ListOfDigits(n))=5); # Muniru A Asiru, Feb 27 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 5];

Select[Range[1000], Max[IntegerDigits[#]] == 5 &] (* Giovanni Resta, Mar 19 2017 *)

for(n=1, 500, if(vecmax(digits(n))==5, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

nxt(n) = {my(d = digits(n), i, j=0, t=0); forstep(i=#d,1,-1, if(d[i]!=5, j=i; break)); if(j>0, d[j]++; if(d[j]==5, for(k=j+1,#d,d[k]=0)); if(j<#d && d[j+1]==5, for(k=j+1,#d-1,d[k]=0)); for(k=1,j-1, if(d[k]==5,for(i=j+1, #d, d[i] = 0);break)), d = vector(#d+1); d[1]=1; d[#d]=5);sum(i=1, #d, d[i]*10^(#d-i))} \\ David A. Corneth, Mar 25 2017

from sympy.ntheory.factor_ import digits
print([n for n in range(1, 501) if max(digits(n)[1:])==5]) # Indranil Ghosh, Mar 19 2017

A283609 Numbers whose largest decimal digit is 6.

Original entry on oeis.org

6, 16, 26, 36, 46, 56, 60, 61, 62, 63, 64, 65, 66, 106, 116, 126, 136, 146, 156, 160, 161, 162, 163, 164, 165, 166, 206, 216, 226, 236, 246, 256, 260, 261, 262, 263, 264, 265, 266, 306, 316, 326, 336, 346, 356, 360, 361, 362, 363, 364, 365, 366, 406, 416, 426

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 6.
Number of terms less than 10^n is 7^n - 6^n.
Prime terms are in A106096.

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Cf. A054055, A106096.

Cf. Sequences of numbers whose largest decimal digit is k (for k = 1..9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), A283608 (k = 5), this sequence (k = 6), A283610 (k = 7), A283611 (k = 8), A011539 (k = 9).

Filtered([1..500],n->Maximum(ListOfDigits(n))=6); # Muniru A Asiru, Mar 01 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 6]

Select[Range[1000], Max[IntegerDigits[#]] == 6 &] (* Giovanni Resta, Mar 19 2017 *)

for(n=1, 500, if(vecmax(digits(n))==6, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

from sympy.ntheory.factor_ import digits
print([n for n in range(1, 501) if max(digits(n)[1:])==6]) # Indranil Ghosh, Mar 19 2017

A283610 Numbers n whose largest decimal digit is 7.

Original entry on oeis.org

7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 107, 117, 127, 137, 147, 157, 167, 170, 171, 172, 173, 174, 175, 176, 177, 207, 217, 227, 237, 247, 257, 267, 270, 271, 272, 273, 274, 275, 276, 277, 307, 317, 327, 337, 347, 357, 367, 370, 371, 372

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 7.
Number of terms less than 10^n is 8^n - 7^n.
Prime terms are in A106095.

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Cf. A054055, A106095.

Cf. Sequences of numbers n whose largest decimal digit is k (for k = 1 - 9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), A283608 (k = 5), A283609 (k = 6), this sequence (k = 7), A283611 (k = 8), A011539 (k = 9).

Filtered([1..380],n->Maximum(ListOfDigits(n))=7); # Muniru A Asiru, Feb 27 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 7]

Select[Range[1000], Max[IntegerDigits[#]] == 7 &] (* Giovanni Resta, Mar 19 2017 *)

for(n=1, 500, if(vecmax(digits(n))==7, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

from sympy.ntheory.factor_ import digits
[n for n in range(1, 401) if max(digits(n)[1:]) == 7]  # Indranil Ghosh, Mar 19 2017

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A083895 Number of divisors of n with largest digit = 8 (base 10).

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A283608 Numbers whose largest decimal digit is 5.

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A283609 Numbers whose largest decimal digit is 6.

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GAP

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A283610 Numbers n whose largest decimal digit is 7.

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GAP

Magma

Mathematica

PARI

Python