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.

Previous Showing 11-17 of 17 results.

A062679 Numbers such that every divisor (except 1, but including the number itself) contains the digit 9.

Original entry on oeis.org

19, 29, 59, 79, 89, 97, 109, 139, 149, 179, 191, 193, 197, 199, 229, 239, 269, 293, 349, 359, 379, 389, 397, 409, 419, 439, 449, 479, 491, 499, 509, 569, 593, 599, 619, 659, 691, 709, 719, 739, 769, 797, 809, 829, 839, 859, 907, 911, 919, 929, 937, 941, 947
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Comments

Different from A106093. 1691 = 19 * 89 is the smallest term that is not in A106093. - Franklin T. Adams-Watters, Apr 30 2007

Examples

			7961 has divisors 19, 419 and 7961, all of which contain the digit 9.

Links

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062680.

Programs

  • Magma
    [n: n in [2..1000] | forall{Divisors(n)[i]: i in [2..NumberOfDivisors(n)] | 9 in Intseq(Divisors(n)[i])}]; // Bruno Berselli, Nov 21 2015
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1000], fQ[#, 9] &] (* Robert G. Wilson v, Jun 11 2014 *)
d9Q[n_]:=First[Union[DigitCount[#,10,9]&/@Rest[Divisors[n]]]]>0; Select[ Range[ 2,1000],d9Q] (* Harvey P. Dale, Sep 12 2014 *)
  • PARI
    isok(n) = {if (n==1, return (0)); d = divisors(n); for (k=1, #d, if ((d[k] != 1) && (vecmax(digits(d[k])) != 9), return (0));); return (1);} \\ Michel Marcus, Nov 21 2015

A062680 Composite numbers whose divisors (except 1) all contain the digit 9.

Original entry on oeis.org

1691, 2291, 3629, 5191, 5539, 5597, 6931, 7391, 7921, 7961, 8497, 8791, 9101, 9329, 9409, 9481, 9671, 9701, 10981, 10991, 11269, 13129, 13891, 14239, 15089, 15931, 15941, 16999, 17197, 17309, 17879, 17951, 17993, 18091, 18449, 18829, 18943
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Examples

			7961 has divisors 19, 419 and 7961, all of which contain the digit 9.

Links

Crossrefs

Composite members of A062679.
Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678.

Programs

  • Magma
    [k:k in [2..20000]|  not IsPrime(k) and forall{d:d in Set(Divisors(k)) diff {1}| 9 in Intseq(d)}];// Marius A. Burtea, Nov 07 2019
  • Mathematica
    fQ[n_] := Union[Drop[Last /@ Sort /@ IntegerDigits[ Divisors[ n]], 1]] == {9}; Select[ Range[ 19110], fQ[ # ] == True && ! PrimeQ[ # ] &] (* Zak Seidov and Robert G. Wilson v, May 17 2005 *)
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 19110], !PrimeQ[#] && fQ[#, 9] &] (* Robert G. Wilson v, Jun 11 2014 *)

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 16 2007

A062653 Every divisor (except 1) contains the digit 2.

Original entry on oeis.org

2, 23, 29, 127, 211, 223, 227, 229, 233, 239, 241, 251, 254, 257, 263, 269, 271, 277, 281, 283, 293, 421, 422, 482, 502, 521, 523, 526, 529, 542, 562, 727, 821, 823, 827, 829, 842, 929, 1021, 1042, 1123, 1129, 1201, 1213, 1217, 1223, 1229, 1231, 1237
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Examples

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

Links

Crossrefs

Cf. A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

  • Magma
    [k:k in [2..1300]| forall{d:d in Set(Divisors(k)) diff {1}| 2 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1300], fQ[#, 2] &]  (* Robert G. Wilson v, Jun 11 2014 *)
  • PARI
    has2(n)=if(n==1, return(1)); !!setsearch(Set(digits(n)),2)
is(n)=fordiv(n,d, if(!has2(d), return(0))); 1 \\ Charles R Greathouse IV, Jan 24 2020

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019

A062668 Composite and every divisor (except 1) contains the digit 3.

Original entry on oeis.org

39, 93, 309, 339, 393, 403, 713, 933, 939, 993, 1137, 1293, 1317, 1329, 1333, 1339, 1369, 1389, 1643, 1703, 1839, 1893, 2263, 2319, 2369, 2573, 3013, 3029, 3039, 3071, 3093, 3099, 3107, 3117, 3139, 3151, 3189, 3193, 3197, 3279, 3309, 3369, 3419, 3459
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, A062667, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

  • Magma
    [k:k in [2..3500]| forall{d:d in Set(Divisors(k)) diff {1}| 3 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 3460], !PrimeQ[#] && fQ[#, 3] &] (* Robert G. Wilson v, Jun 11 2014 *)

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019

A257668 Primes containing a 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, 547, 557, 571, 577, 587, 607, 617, 647, 673, 677, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761
Offset: 1

Views

Author

Vincenzo Librandi, May 03 2015

Keywords

Comments

Primes in A062675.
Subsequence of primes of A011537. - Michel Marcus, May 03 2015

Examples

			For n = 2, a(2) = 17 is the second prime containing a digit of 7.

Links

Crossrefs

Cf. similar sequences listed in A257667.
Cf. A011537, A062675, A166579 (subsequence).

Programs

  • Magma
    [p: p in PrimesUpTo(800) | 7 in Intseq(p)];
  • Mathematica
    Select[Prime[Range[150]], ! StringFreeQ[ToString[#], "7"] &]
  • PARI
    lista(nn) = forprime(p=2, nn, if(vecsearch(vecsort(digits(p)), 7), print1(p, ", "))); \\ Altug Alkan, Apr 21 2016; corrected by Michel Marcus, Oct 30 2023
  • Sage
    [p for p in primes(800) if 7 in p.digits(base=10)] # Bruno Berselli, May 03 2015

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Nov 01 2022

A062649 Composite numbers with property that every divisor contains the digit 1.

Original entry on oeis.org

121, 143, 169, 187, 221, 341, 361, 451, 671, 781, 961, 1037, 1111, 1133, 1159, 1177, 1199, 1207, 1243, 1271, 1313, 1331, 1339, 1349, 1391, 1397, 1417, 1441, 1469, 1507, 1529, 1573, 1639, 1651, 1661, 1681, 1703, 1717, 1727, 1751, 1781, 1793, 1807, 1819
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Comments

Intersection of A002808 and A062634. - Michel Marcus, Sep 12 2013

Examples

			143 has divisors 1, 11, 13 and 143, all of which contain the digit 1.

Links

Crossrefs

Cf. A062634, A062653, A062664, A062667, 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, 1850], !PrimeQ[#] && fQ[#, 1] &] (* Robert G. Wilson v, Jun 11 2014 *)
  • PARI
    lista(nn) = {forcomposite(n = 1, nn, ok = 1; fordiv(n, d, ok = ok && setsearch(Set(digits(d)), 1)); if (ok, print1(n, ", ")););} \\ Michel Marcus, Sep 12 2013

A243825 Numbers n such that every divisor greater than 1 contains the digit 0.

Original entry on oeis.org

101, 103, 107, 109, 307, 401, 409, 503, 509, 601, 607, 701, 709, 809, 907, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1201, 1301, 1303, 1307, 1409, 1601, 1607, 1609, 1709, 1801, 1901, 1907, 2003, 2011, 2017, 2027, 2029
Offset: 1

Views

Author

Barbara W. Waddell and Robert G. Wilson v, Jun 11 2014

Keywords

Comments

This is an example of a composite number in the sequence which demonstrates that A056709 is a proper subsequence. - R. J. Mathar, Jun 13 2014

Examples

			The divisors of 10201 are {1, 101 & 10201}. Except for 1 each has a 0 in its decimal expansion.

Links

Crossrefs

Cf. A062634, A062653, A062667, A062669, A062671, A062673, A062675, A062677, A062679.
Supersequence of A056709 (primes) and A243819 (composites).

Programs

  • Magma
    [m:m in [2..2100] |  #[d:d in Divisors(m)|0 in Intseq(d)] eq #Divisors(m)-1]; // Marius A. Burtea, Nov 08 2019
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 2030], fQ[#, 0] &]
Previous Showing 11-17 of 17 results.

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

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