cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 17 results. Next

A062664 Composite and every divisor (except for 1) contains the digit 2.

Original entry on oeis.org

254, 422, 482, 502, 526, 529, 542, 562, 842, 1042, 1642, 2042, 2246, 2258, 2402, 2426, 2434, 2446, 2458, 2462, 2474, 2498, 2518, 2554, 2558, 2566, 2578, 2582, 2594, 2642, 2654, 2846, 2854, 2858, 2921, 3242, 3254, 3442, 4022, 4126, 4162, 4222, 4226
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Comments

If k is in the sequence, then all composite divisors of k are in the sequence. - Robert Israel, Jul 11 2019

Examples

			254 has divisors 1, 2, 127 and 254, all of which except for 1 contain the digit 2.

Links

Crossrefs

Cf. A062649, A062668, A062670, A062672, A062674, A062676, A062678, A062680, A243819.

Programs

  • Magma
    [m:m in [2..4300] | not IsPrime(m) and #[d:d in Divisors(m)|2 in Intseq(d)] eq #Divisors(m)-1]; // Marius A. Burtea, Jul 11 2019
  • Maple
    filter:= proc(n) local D;
  if isprime(n) then return false fi;
  andmap(con2,numtheory:-divisors(n) minus {1})
end proc:
con2:= proc(n) option remember; member(2,convert(n,base,10)) end proc:
select(filter, [$4..10000]);# Robert Israel, Jul 11 2019
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 4230], !PrimeQ[#] && fQ[#, 2] &] (* Robert G. Wilson v, Jun 11 2014 *)

Extensions

Offset changed by Robert Israel, Jul 11 2019

A062667 Every divisor (except 1) contains the digit 3.

Original entry on oeis.org

3, 13, 23, 31, 37, 39, 43, 53, 73, 83, 93, 103, 113, 131, 137, 139, 163, 173, 193, 223, 233, 239, 263, 283, 293, 307, 309, 311, 313, 317, 331, 337, 339, 347, 349, 353, 359, 367, 373, 379, 383, 389, 393, 397, 403, 431, 433, 439, 443, 463, 503, 523, 563, 593
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Examples

			93 has divisors 1, 3, 31 and 93, all of which contain the digit 3.

Links

Crossrefs

Cf. A062653, A062664, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 600], fQ[#, 3] &]  (* Robert G. Wilson v, Jun 11 2014 *)
Select[Range[2,600],AllTrue[Flatten[DigitCount[#,10,3]&/@Rest[Divisors[#]]],#>0&]&] (* Harvey P. Dale, Oct 04 2024 *)

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019

A062669 Every divisor (except 1) contains the digit 4.

Original entry on oeis.org

41, 43, 47, 149, 241, 347, 349, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 541, 547, 641, 643, 647, 743, 941, 947, 1049, 1249, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Examples

			1849 has divisors 1, 43 and 1849, the last two of which contain the digit 4.

Links

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

  • Magma
    [k:k in [2..1500]| forall{d:d in Set(Divisors(k)) diff {1}| 4 in Intseq(d)}];// Marius A. Burtea, Nov 07 2019
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1500], fQ[#, 4] &] (* Robert G. Wilson v, Jun 11 2014 *)
Select[Range[2,1500],AllTrue[Rest[Divisors[#]],DigitCount[#,10,4]>0&]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 05 2021 *)

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019
Example corrected by Harvey P. Dale, Jun 05 2021

A062670 Composite and every divisor (except 1) contains the digit 4.

Original entry on oeis.org

1849, 6407, 14227, 14309, 14921, 16403, 16441, 17243, 18409, 18847, 19049, 19147, 20459, 20941, 21457, 21479, 21949, 22427, 23453, 25427, 27649, 30409, 30463, 31949, 34921, 40463, 40721, 43009, 44227, 44509, 45107, 49303, 58343, 59491
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Examples

			1849 has divisors 1, 43 and 1849, all of which contain the digit 4.

Links

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 59500], !PrimeQ[#] && fQ[#, 4] &] (* Robert G. Wilson v, Jun 11 2014 *)
d4Q[n_]:=CompositeQ[n]&&AllTrue[Rest[Divisors[n]],DigitCount[#,10,4]>0&]; Select[Range[ 60000],d4Q] (* Harvey P. Dale, Jun 20 2023 *)

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019

A062671 Every divisor (except 1) contains the digit 5.

Original entry on oeis.org

5, 25, 53, 59, 125, 151, 157, 251, 257, 265, 295, 353, 359, 457, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 625, 653, 659, 751, 755, 757, 785, 853, 857, 859, 953, 1051, 1151, 1153, 1255, 1259, 1285, 1325, 1451, 1453, 1459, 1475, 1511
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Examples

			25 has divisors 1, 5 and 25, all of which (except 1) contain the digit 5.

Links

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

  • Magma
    [k:k in [2..1500]| forall{d:d in Set(Divisors(k)) diff {1}| 5 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1500], fQ[#, 5] &] (* Robert G. Wilson v, Jun 11 2014 *)
  • Python
    from sympy import divisors
def ok(n): return all('5' in str(d) for d in divisors(n)[1:])
print(list(filter(ok, range(2, 1512)))) # Michael S. Branicky, May 25 2021

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019

A062672 Composite and every divisor (except 1) contains the digit 5.

Original entry on oeis.org

25, 125, 265, 295, 625, 755, 785, 1255, 1285, 1325, 1475, 1765, 1795, 2285, 2515, 2545, 2605, 2615, 2705, 2735, 2785, 2815, 2845, 2855, 2885, 2935, 2965, 2995, 3125, 3265, 3295, 3755, 3775, 3785, 3925, 4265, 4285, 4295, 4765, 5255, 5755, 5765, 6275
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Examples

			25 has divisors 1, 5 and 25, all of which contain the digit 5.

Links

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 6300], !PrimeQ[#] && fQ[#, 5] &] (* Robert G. Wilson v, Jun 11 2014 *)
Select[Range[6300],CompositeQ[#]&&AllTrue[Rest[Divisors[#]],DigitCount[ #,10,5]> 0&]&] (* Harvey P. Dale, Jan 22 2023 *)

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019

A062673 Every divisor (except 1) contains the digit 6.

Original entry on oeis.org

61, 67, 163, 167, 263, 269, 367, 461, 463, 467, 563, 569, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 761, 769, 863, 967, 1061, 1063, 1069, 1163, 1361, 1367, 1567, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Examples

			26569 has divisors 163 and 26569, each of which contains the digit 6.

Links

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

  • Magma
    [k:k in [2..1700]| forall{d:d in Set(Divisors(k)) diff {1}| 6 in Intseq(d)}];// Marius A. Burtea, Nov 07 2019
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1660], fQ[#, 6] &] (* Robert G. Wilson v, Jun 11 2014 *)
Select[Range[2,2000],AllTrue[Rest[Divisors[#]],DigitCount[#,10,6]>0&]&] (* Harvey P. Dale, Jul 14 2025 *)

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019

A062674 Composite and every divisor (except 1) contains the digit 6.

Original entry on oeis.org

16043, 16409, 17621, 26569, 36661, 37637, 39467, 40267, 40669, 41663, 42869, 45761, 46297, 46421, 46909, 52643, 61289, 64721, 64789, 64843, 65209, 69169, 71623, 72361, 75469, 76121, 76987, 91769, 96521, 97661, 97963, 100367, 101369
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Examples

			26569 has divisors 163 and 26569, all of which contain the digit 6.

Links

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

  • Mathematica
    Select[Range[2,102000],!PrimeQ[#]&&And@@(MemberQ[IntegerDigits[#], 6]&/@ Rest[Divisors[#]])&] (* Harvey P. Dale, May 26 2013 *)
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 101400], !PrimeQ[#] && fQ[#, 6] &] (* Robert G. Wilson v, Jun 11 2014 *)

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019

A062675 Every divisor (except 1) contains the digit 7.

Original entry on oeis.org

7, 17, 37, 47, 67, 71, 73, 79, 97, 107, 127, 137, 157, 167, 173, 179, 197, 227, 257, 271, 277, 307, 317, 337, 347, 367, 373, 379, 397, 457, 467, 479, 487, 497, 547, 557, 571, 577, 587, 607, 617, 647, 673, 677, 679, 701, 709, 719, 727, 733, 739, 743, 749, 751
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Examples

			799 has divisors 17, 47 and 799, all of which contain the digit 7.

Links

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062676, A062677, A062678, A062679, A062680.

Programs

  • Magma
    [k:k in [2..800]| forall{d:d in Set(Divisors(k)) diff {1}| 7 in Intseq(d)}];// Marius A. Burtea, Nov 07 2019
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 760], fQ[#, 7] &]  (* Robert G. Wilson v, Jun 11 2014 *)

A062677 Numbers with property that every divisor (except 1) contains the digit 8.

Original entry on oeis.org

83, 89, 181, 281, 283, 383, 389, 487, 587, 683, 787, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 983, 1087, 1181, 1187, 1283, 1289, 1381, 1481, 1483, 1487, 1489, 1583, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Comments

Subsequence of A011538, numbers with an 8. - Michel Marcus, Nov 21 2015

Examples

			7387 has divisors 83, 89 and 7387, all of which contain the digit 8.

Links

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062678, A062679, A062680.

Programs

  • Maple
    isA062677 := proc(n)
    if n = 1 then
        return false;
    end if;
    for d in numtheory[divisors](n) minus {1} do
        convert(convert(d,base,10),set) ;
        if  not 8 in % then
            return false;
        end if;
    end do:
    true ;
end proc:
for n from 1 to 2000 do
    if isA062677(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Mar 27 2017
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1900], fQ[#, 8] &] (* Robert G. Wilson v, Jun 11 2014 *)
Showing 1-10 of 17 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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