A038772 -id:A038772 - cp's OEIS frontend

A054476 Numbers not divisible by any of their digits when written in base 5.

13, 17, 19, 23, 53, 65, 67, 73, 77, 79, 85, 89, 94, 95, 97, 98, 103, 113, 115, 118, 119, 253, 263, 265, 269, 313, 317, 319, 323, 325, 329, 335, 337, 343, 347, 349, 353, 365, 367, 373, 377, 379, 385, 389, 394, 395, 397, 398, 425, 427, 437, 439, 443, 445, 449

Offset: 1

Henry Bottomley, May 12 2000

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A038772, A055239, A055240.

is(n)=my(d=Set(digits(n,5))); for(i=if(d[1],1,2),#d, if(n%d[i]==0, return(0))); 1 \\ Charles R Greathouse IV, Feb 23 2017

A082947 Palindromes not divisible by any of their digits.

Original entry on oeis.org

323, 343, 353, 373, 383, 434, 454, 474, 494, 646, 656, 676, 686, 727, 737, 747, 757, 767, 787, 797, 838, 858, 868, 878, 898, 929, 949, 959, 969, 979, 989, 3223, 3443, 3553, 3883, 4334, 4554, 4994, 6446, 6556, 6886, 7227, 7337, 7447, 7557, 7667, 7887, 7997

Offset: 1

Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

Intersection of A002113 and A038772. - Michel Marcus, Mar 07 2015

			969 is a member of the sequence since it is neither divisible by 9 nor 6 but 8778 is not since it is divisible by 7.

Suggested by Amarnath Murthy.

Cf. A002113 (palindromes in base 10), A038772 (numbers not divisible by any of their digits).

DeleteCases[Select[Range[9000],PalindromeQ],?(AnyTrue[#/Union[ IntegerDigits[ #]],IntegerQ]&)]//Quiet (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale, Mar 05 2018 *)

isok(n) = {d = digits(n); if (Vecrev(d) == d, for (i=1, #d, if (d[i] && !(n % d[i]), return (0));); return (1););} \\ Michel Marcus, Mar 07 2015

A147963 a(n) = number of n-digit numbers not divisible by any of their digits.

Original entry on oeis.org

0, 31, 244, 2012, 16831, 142224, 1212521, 10412937, 89964007, 781192156, 6812648578, 59632654665, 523659800584, 4611408084221, 40708677441051, 360148330033068, 3192319968308509, 28344332639409466, 252044515540416543, 2244223537121190033, 20006367211775121313

Offset: 1

Zak Seidov, Nov 17 2008

Numbers ending in 0 are ignored.

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100

Cf. A038772 Numbers not divisible by any of their digits.

a[n_] := (c = 0; Do[id = IntegerDigits[i]; Le = Length[id]; pr = Product[If[id[[k]] > 0, Mod[i, id[[k]]], 1], {k, Le}]; If[Mod[i, 10]*pr > 0,(*Print[n];*)c++ ], {i, 10^(n - 1), 10^n - 1}]; c); a[1] = 0; Table[a[m], {m, 8}]

a(10)-a(11) from Sean A. Irvine, Nov 11 2010
a(12) from Donovan Johnson, Nov 14 2010
a(13)-a(21) from Hiroaki Yamanouchi, Aug 31 2014

A176659 Partial sums of A038770.

Original entry on oeis.org

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 277, 302, 328, 356, 386, 417, 449, 482, 517, 553, 592, 632, 673, 715, 759, 804, 852, 902, 953, 1005, 1060, 1120, 1181, 1243, 1306, 1370, 1435, 1501, 1571, 1642

Offset: 1

Jonathan Vos Post, Apr 23 2010

Partial sums of numbers divisible by at least one of their digits. Identical to triangular numbers A000217 until a(23), then differs, because 23 is the smallest natural number in the complement of A038770 (A038772, i.e., not divisible by at least one of its digits). Hence this partial sum is the triangular numbers minus the partial sums of A038772, properly offset. The subsequence of primes (of course 3 is the largest prime triangular number) in the partial sum begins: 3, 277, 449, 673, 953, 1181, 1571, 1789, 2027. What are the equivalents in bases other than 10?

			a(23) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 24 = 277 is prime.

Cf. A038770, A034709, A034837, A038769, A038772.

Accumulate[Select[Range[110],MemberQ[Divisible[#,Cases[ IntegerDigits[ #], Except[ 0]]], True]&]] (* Harvey P. Dale, May 11 2017 *)

a(n) = Sum_{i=1..n} A038770(i).

A188454 Numbers n whose decimal digits are distinct and no digit divides n.

Original entry on oeis.org

23, 27, 29, 34, 37, 38, 43, 46, 47, 49, 53, 54, 56, 57, 58, 59, 67, 68, 69, 73, 74, 76, 78, 79, 83, 86, 87, 89, 94, 97, 98, 203, 207, 209, 239, 247, 249, 253, 257, 259, 263, 267, 269, 283, 289, 293, 307, 308, 329, 346, 347, 349, 356, 358, 359, 367, 370, 374

Offset: 1

Andy Edwards, Mar 31 2011

These may not contain 1 or have a 2 or 5 as the last digit. They include prime numbers not containing the digit 1 and composites with a smallest prime factor > 10 and obeying the other constraints (e.g. the largest case is 987654203 = 31*31859813).
The first even case is 34. The first consecutive pair is {37, 38}. {56,57,58,59} is a consecutive quadruple which is the maximal size for such a subset.
There are 202623 terms in this sequence. - Nathaniel Johnston, May 19 2011

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A038772, A034709, A034837, A038769, A038770.

dddQ[n_]:=Module[{dcn=DigitCount[n]},Max[dcn]==1&&First[dcn]==0 && Union[ Divisible[n,Select[IntegerDigits[n],#!=0&]]]=={False}]; Select[Range[ 400],dddQ] (* Harvey P. Dale, May 01 2012 *)

A331342 Lexicographically earliest sequence of distinct terms a(n) indivisible by all of their digits that become divisible by all of their digits when a(n+1) is added to a(n).

Original entry on oeis.org

23, 43, 34, 54, 57, 58, 53, 46, 69, 59, 29, 37, 74, 38, 73, 49, 79, 47, 68, 56, 76, 86, 89, 223, 389, 247, 377, 67, 257, 367, 269, 97, 27, 397, 227, 439, 233, 379, 293, 343, 323, 289, 347, 277, 359, 253, 83, 229, 259, 353, 283, 329, 337, 87, 249, 239, 94, 338, 334, 78, 346, 98, 457, 479, 634, 477, 638

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Jan 14 2020

Is this sequence a reordering of A038772?

			a(1) = 23 is not divisible by 2 and not divisible by 3. When a(2) = 43 is added to a(1) = 23, the result (66) is divisible by all its digits.
a(2) = 43 is not divisible by 4 and not divisible by 3. When a(3) = 34 is added to a(2) = 43, the result (77) is divisible by all its digits.
a(3) = 34 is not divisible by 3 and not divisible by 4. When a(4) = 54 is added to a(3) = 34, the result (88) is divisible by all its digits.
a(4) = 54 is not divisible by 5 and not divisible by 4. When a(5) = 57 is added to a(4) = 54, the result (111) is divisible by all its digits.
a(5) = 57 is not divisible by 5 and not divisible by 7. When a(6) = 58 is added to a(5) = 57, the result (115) is divisible by all its digits....

Jean-Marc Falcoz, Table of n, a(n) for n = 1..20001

Cf. A038772, A034838.

A342844 Composite numbers not divisible by any of their nonzero digits.

Original entry on oeis.org

27, 34, 38, 46, 49, 54, 56, 57, 58, 68, 69, 74, 76, 78, 86, 87, 94, 98, 203, 207, 209, 247, 249, 253, 259, 267, 289, 299, 308, 323, 329, 334, 338, 343, 346, 356, 358, 370, 374, 376, 377, 380, 386, 388, 394, 398, 403, 406, 407, 429, 430, 434, 437, 446, 447, 454

Offset: 1

John Bibby, Mar 24 2021

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A038772, A316227.

q:= n-> not isprime(n) and andmap(d-> irem(n, d)>0,
        {convert(n, base, 10)[]} minus {0}):
select(q, [$1..500])[];  # Alois P. Heinz, Apr 01 2021

Select[Range@500,!PrimeQ@#&&Mod[#,DeleteCases[IntegerDigits@#,0]]~FreeQ~0&] (* Giorgos Kalogeropoulos, Apr 01 2021 *)
Select[Range[500],CompositeQ[#]&&NoneTrue[#/(IntegerDigits[#]/.(0-> Nothing)),IntegerQ]&] (* Harvey P. Dale, Dec 28 2021 *)

isok(n)={if(isprime(n), 0, my(v=digits(n)); for(i=1, #v, if(v[i]<>0 && n%v[i]==0, return(0))); 1)} \\ Andrew Howroyd, Mar 25 2021

from sympy import isprime
def ok(n): return not isprime(n) and all(n%int(d) for d in str(n) if d!='0')
print(list(filter(ok, range(4, 455)))) # Michael S. Branicky, Apr 01 2021

A054475 Numbers not divisible by any of their digits when written in base 4.

Original entry on oeis.org

11, 35, 43, 47, 59, 131, 139, 143, 163, 175, 179, 187, 191, 203, 227, 235, 239, 251, 515, 523, 527, 547, 559, 563, 571, 575, 643, 655, 683, 691, 703, 707, 715, 719, 739, 751, 755, 763, 767, 779, 803, 811, 815, 827, 899, 907, 911, 931, 943, 947, 955, 959

Offset: 1

Henry Bottomley, May 12 2000

Cf. A038772, A055239, A055240.

A054478 Numbers not divisible by any of their digits when written in base 6.

Original entry on oeis.org

17, 22, 23, 29, 34, 77, 89, 101, 107, 113, 130, 131, 137, 142, 143, 149, 161, 166, 167, 173, 174, 178, 179, 197, 202, 203, 209, 214, 437, 449, 461, 467, 509, 521, 527, 533, 539, 557, 563, 569, 581, 593, 599, 611, 617, 629, 641, 647, 653, 670, 671, 677, 682

Offset: 1

Henry Bottomley, May 12 2000

Cf. A038772, A055239, A055240.

A054484 Numbers not divisible by any of their digits when written in base 7.

Original entry on oeis.org

17, 19, 23, 25, 26, 31, 33, 34, 37, 38, 39, 41, 46, 47, 101, 103, 115, 117, 119, 121, 125, 131, 133, 137, 139, 143, 149, 151, 152, 161, 163, 167, 173, 175, 178, 179, 181, 182, 187, 188, 191, 193, 194, 199, 201, 202, 217, 221, 223, 227, 229, 230, 231, 233, 237

Offset: 1

Henry Bottomley, May 12 2000

Cf. A038772, A055239, A055240.

cp's OEIS Frontend

A054476 Numbers not divisible by any of their digits when written in base 5.

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A082947 Palindromes not divisible by any of their digits.

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A147963 a(n) = number of n-digit numbers not divisible by any of their digits.

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A176659 Partial sums of A038770.

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A188454 Numbers n whose decimal digits are distinct and no digit divides n.

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A331342 Lexicographically earliest sequence of distinct terms a(n) indivisible by all of their digits that become divisible by all of their digits when a(n+1) is added to a(n).

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A342844 Composite numbers not divisible by any of their nonzero digits.

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A054475 Numbers not divisible by any of their digits when written in base 4.

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A054478 Numbers not divisible by any of their digits when written in base 6.

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A054484 Numbers not divisible by any of their digits when written in base 7.

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