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 1-4 of 4 results.

A035139 Digits of prime factors of k do not appear in k.

Original entry on oeis.org

1, 4, 6, 8, 9, 10, 14, 16, 18, 21, 27, 34, 38, 40, 44, 46, 48, 49, 54, 56, 57, 58, 60, 64, 66, 68, 69, 76, 78, 80, 81, 84, 86, 87, 88, 90, 96, 98, 99, 100, 106, 108, 111, 116, 118, 129, 134, 140, 144, 146, 148, 158, 160, 161, 166, 168, 174, 177, 180, 184, 188, 189, 196
Offset: 1

Views

Author

Patrick De Geest, Nov 15 1998

Keywords

Examples

			161 = 7 * 23 since {2,3,7} and {1,6} are separate digit sets.

Links

Crossrefs

Cf. A035140, A035141.

Programs

  • Magma
    [k:k in [1..200]| forall{a: a in PrimeDivisors(k)|Set(Intseq(a)) meet Set(Intseq(k)) eq {}}]; // Marius A. Burtea, Oct 08 2019
  • Maple
    q:= n-> (f-> is(map(f, numtheory[factorset](n)) intersect
        {f(n)}={}))(d-> convert(d, base, 10)[]):
select(q, [$1..200])[];  # Alois P. Heinz, Oct 11 2021
  • Mathematica
    Fac[n_] := Flatten[IntegerDigits[Take[FactorInteger[n],All,1]]]; t={1}; Do[ If[!PrimeQ[n] && Intersection[Fac[n], IntegerDigits[n]] == {}, AppendTo[t,n]], {n,2,196}]; t (* Jayanta Basu, May 02 2013 *)
  • PARI
    digsf(n) = my(f=factor(n), list=List()); for (k=1, #f~, my(dk=digits(f[k,1])); for (i=1, f[k,2], for (j=1, #dk, listput(list, dk[j])))); Vec(list);
isok(m) = my(df=digsf(m), d=digits(m)); (#setintersect(Set(df), Set(d)) == 0); \\ Michel Marcus, Oct 11 2021
  • Python
    from sympy import factorint
def ok(n):
    return set(str(n)) & set("".join(str(p) for p in factorint(n))) == set()
print(list(filter(ok, range(1601))))  # Michael S. Branicky, Oct 11 2021

Extensions

Offset corrected and a(1) added by Giovanni Resta, May 02 2013

A035140 Digits of juxtaposition of prime factors of composite n appear also in n.

Original entry on oeis.org

25, 32, 121, 125, 128, 132, 135, 143, 175, 187, 243, 250, 256, 295, 312, 324, 341, 351, 375, 432, 451, 512, 625, 671, 679, 735, 781, 875, 928, 932, 1023, 1024, 1053, 1057, 1207, 1243, 1250, 1255, 1324, 1325, 1328, 1331, 1352, 1359, 1372, 1375, 1377, 1379
Offset: 1

Views

Author

Patrick De Geest, Nov 15 1998

Keywords

Examples

			295 = 5 * 59 since {5,9} is a subset of {2,5,9}.

Links

Crossrefs

Cf. A035139, A035141.

Programs

  • Mathematica
    id[n_]:=Complement[Range[0,9],IntegerDigits[n]]; fac[n_]:=Flatten[IntegerDigits[Take[FactorInteger[n],All,1]]]; t={}; Do[If[!PrimeQ[n] && Intersection[id[n],fac[n]] == {}, AppendTo[t,n]], {n,2,1380}]; t (* Jayanta Basu, May 01 2013 *)
Select[Range@10000, CompositeQ@# && SubsetQ[IntegerDigits@#,Flatten@IntegerDigits@(#[[1]] & /@ FactorInteger@#)] &] (* Hans Rudolf Widmer, May 11 2023 *)
  • Python
    from sympy import factorint, isprime
def ok(n): return n > 1 and not isprime(n) and set("".join(str(p) for p in factorint(n))) <= set(str(n))
print([k for k in range(1380) if ok(k)]) # Michael S. Branicky, May 11 2023

Extensions

Name clarified by Hans Rudolf Widmer, May 11 2023

A372384 The smallest composite number k such that the digits of k and its prime factors, both written in base n, contain the same set of distinct digits.

Original entry on oeis.org

4, 8, 30, 25, 57, 16, 27, 192, 132, 121, 185, 169, 465, 32, 306, 289, 489, 361, 451, 2250, 552, 529, 125, 1586, 81, 1652, 985, 841, 1057, 64, 1285, 86166, 2555, 1332, 1387, 1369, 4752, 3240, 2005, 1681, 2649, 1849, 2047, 5456, 2256, 2209, 343, 5050, 2761, 5876, 2862, 2809, 3097, 15512
Offset: 2

Views

Author

Scott R. Shannon, Apr 29 2024

Keywords

Examples

			a(4) = 30 as 30 = 2 * 3 * 5 = 132_4 = 2_4 * 3_4 * 11_4, and both 132_4 and its prime factors contain the same distinct digits 1, 2, and 3.
a(10) = 132 as 132 = 2 * 3 * 11, and both 132 and its prime factors contain the same distinct digits 1, 2, and 3. See also A035141.
a(14) = 465 as 465 = 3 * 5 * 31 = 253_14 = 3_14 * 5_14 * 23_14, and both 253_14 and its prime factors contain the same distinct digits 2, 3, and 5.

Links

Crossrefs

Cf. A027746, A035141, A035140, A372309, A371695, A000668.

Formula

a(n) = 2*n + 2 if n = 2^k - 1 with k >= 2, otherwise a(n) = n^2 if n is prime.

A237713 Composite numbers n such that the distinct digits in n and the distinct digits in the proper divisors of n are the same.

Original entry on oeis.org

125, 1255, 2510, 11009, 11099, 11255, 11379, 12326, 12955, 14379, 14397, 15033, 15303, 16325, 17482, 21109, 25105, 31007, 31503, 33011, 35213, 37127, 37921, 41303, 44011, 49319, 51367, 53491, 63013, 69413, 70319, 71057, 72013, 72517, 74341, 77011, 81767
Offset: 1

Views

Author

Michel Lagneau, Feb 12 2014

Keywords

Comments

Since 1 is always a divisor of n, this is a subsequence of A011531. - Michel Marcus, Feb 12 2014

Examples

			125 is in the sequence because the proper divisors of 125 are {1, 5, 25} with the same digits as 125.

Links

Crossrefs

Cf. A032741, A035141.
See A282755 for a variant.

Programs

  • Mathematica
    Pn[n_]:=Sort[DeleteDuplicates[Flatten[IntegerDigits[Take[Divisors[n],DivisorSigma[0,n]-1]]]]];Fn[n_]:=Sort[DeleteDuplicates[IntegerDigits[n]]];lst={};Do[If[!PrimeQ[n]&&Pn[n]===Fn[n],AppendTo[lst,n]],{n,2,10^5}];lst
Select[Range[10^5], ! PrimeQ@# && Union@ IntegerDigits@ # == Union @@ IntegerDigits /@ Most@ Divisors@ # &] (* Giovanni Resta, Feb 12 2014 *)
  • PARI
    isok(n) = { my(digs = []); fordiv(n, d, if (d != n, digs = concat(digs, digits(d)))); (n != 1) && !isprime(n) && vecsort(digs,,8) == vecsort(digits(n),,8);} \\ Michel Marcus, Feb 12 2014
Showing 1-4 of 4 results.

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