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 1-3 of 3 results.

A037278 Replace n with concatenation of its divisors.

Original entry on oeis.org

1, 12, 13, 124, 15, 1236, 17, 1248, 139, 12510, 111, 1234612, 113, 12714, 13515, 124816, 117, 1236918, 119, 12451020, 13721, 121122, 123, 1234681224, 1525, 121326, 13927, 12471428, 129, 12356101530, 131, 12481632, 131133, 121734, 15735, 123469121836, 137
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

a(n) is the union of A176555(n) for n >= 1 and A176556(n) for n >= 2. See A176553 (numbers m such that concatenations of divisors of m are noncomposites) and A176554 (numbers m such that concatenations of divisors of m are nonprimes). [Jaroslav Krizek, Apr 21 2010]
a(n) is the concatenation of n-th row of the triangle in A027750.

Links

Crossrefs

Cf. A027750, A037283, A037277, A106708.

Programs

  • Haskell
    a037278 = read . concatMap show . a027750_row :: Integer -> Integer
-- Reinhard Zumkeller, Jul 13 2013, May 01 2012, Aug 07 2011
  • MATLAB
    m=1;
for u=1:34 div=divisors(u); conc=str2num(strrep(num2str(div), ' ', ''));
   sol(m)=conc; m=m+1;
end
sol % Marius A. Burtea, Jun 01 2019
  • Magma
    k:=1; sol:=[];
for u in [1..34] do D:=Divisors(u); conc:=D[1];
    for u1 in [2..#D] do a:=#Intseq(conc); a1:=#Intseq(D[u1]); conc:=10^a1*conc+D[u1];end for;
     sol[u]:=conc; k:=k+1;
end for;
sol; // Marius A. Burtea, Jun 01 2019
  • Mathematica
    a[n_] := ToExpression[ StringJoin[ ToString /@ Divisors[n] ] ]; Table[ a[n], {n, 1, 34}] (* Jean-François Alcover, Dec 01 2011 *)
FromDigits[Flatten[IntegerDigits/@Divisors[#]]]&/@Range[40] (* Harvey P. Dale, Nov 09 2012 *)
  • PARI
    a(n) = my(s=""); fordiv(n, d, s = concat(s, Str(d))); eval(s); \\ Michel Marcus, Jun 01 2019 and Sep 22 2022
  • Python
    from sympy import divisors
def a(n): return int("".join(str(d) for d in divisors(n)))
print([a(n) for n in range(1, 35)]) # Michael S. Branicky, Dec 31 2020

Formula

A134681(n) = A055642(a(n)). - Reinhard Zumkeller, Nov 06 2007

Extensions

More terms from Erich Friedman

A106708 a(n) is the concatenation of its nontrivial divisors.

Original entry on oeis.org

0, 0, 0, 2, 0, 23, 0, 24, 3, 25, 0, 2346, 0, 27, 35, 248, 0, 2369, 0, 24510, 37, 211, 0, 2346812, 5, 213, 39, 24714, 0, 23561015, 0, 24816, 311, 217, 57, 234691218, 0, 219, 313, 24581020, 0, 23671421, 0, 241122, 35915, 223, 0, 23468121624, 7, 251025, 317
Offset: 1

Views

Author

N. J. A. Sloane, Jul 20 2007

Keywords

Links

Crossrefs

Cf. A037278, A120712, A037279, A131983 (records), A131984 (where records occur).
Cf. A027750, A010051, A037285, A037277, A163870.

Programs

  • Haskell
    a106708 1           = 0
a106708 n
   | a010051 n == 1 = 0
   | otherwise = read $ concat $ (map show) $ init $ tail $ a027750_row n
-- Reinhard Zumkeller, May 01 2012
  • Maple
    A106708 := proc(n) local dvs ; if isprime(n) or n = 1 then 0; else dvs := [op(numtheory[divisors](n) minus {1,n} )] ; dvs := sort(dvs) ; cat(op(dvs)) ; fi ; end: seq(A106708(n),n=1..80) ; # R. J. Mathar, Aug 01 2007
  • Mathematica
    Table[If[CompositeQ[n],FromDigits[Flatten[IntegerDigits/@Rest[ Most[ Divisors[ n]]]]],0],{n,60}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 22 2020 *)
  • PARI
    {map(n) = local(d); d=divisors(n); if(#d<3, 0, d[1]=""; eval(concat(vecextract(d, concat("..", #d-1)))))}
for(n=1,51,print1(map(n),",")) /* Klaus Brockhaus, Aug 05 2007 */
  • Python
    from sympy import divisors
def a(n):
  nontrivial_divisors = [d for d in divisors(n)[1:-1]]
  if len(nontrivial_divisors) == 0: return 0
  else: return int("".join(str(d) for d in nontrivial_divisors))
print([a(n) for n in range(1, 52)]) # Michael S. Branicky, Dec 31 2020

Formula

a(n) = A037279(n) * A010051(n). - R. J. Mathar, Aug 01 2007

Extensions

More terms from R. J. Mathar and Klaus Brockhaus, Aug 01 2007
Name edited by Michael S. Branicky, Dec 31 2020

A037284 Replace n with concatenation of its odd divisors >1.

Original entry on oeis.org

0, 0, 3, 0, 5, 3, 7, 0, 39, 5, 11, 3, 13, 7, 3515, 0, 17, 39, 19, 5, 3721, 11, 23, 3, 525, 13, 3927, 7, 29, 3515, 31, 0, 31133, 17, 5735, 39, 37, 19, 31339, 5, 41, 3721, 43, 11, 3591545, 23, 47, 3, 749, 525, 31751
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A182469, A209229, A037277, A037283, A037285.

Programs

  • Haskell
    a037284 n
   | a209229 n == 1 = 0
   | otherwise      = read $ concat $ (map show) $ tail $ a182469_row n
-- Reinhard Zumkeller, May 01 2012
  • Mathematica
    Array[FromDigits[Flatten[IntegerDigits/@Rest[Select[Divisors[#], OddQ]]]]&, 60] (* Harvey P. Dale, Mar 03 2014 *)
  • Python
    from sympy import divisors
def a(n):
  odd_divisors_gt1 = [d for d in divisors(n)[1:] if d%2 == 1]
  if len(odd_divisors_gt1) == 0: return 0
  else: return int("".join(str(d) for d in odd_divisors_gt1))
print([a(n) for n in range(1, 52)]) # Michael S. Branicky, Dec 31 2020

Extensions

a(36) corrected by Reinhard Zumkeller, May 01 2012
Showing 1-3 of 3 results.

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

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