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.

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

A182469 Triangle read by rows in which row n lists the odd divisors of n.

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 5, 1, 3, 1, 7, 1, 1, 3, 9, 1, 5, 1, 11, 1, 3, 1, 13, 1, 7, 1, 3, 5, 15, 1, 1, 17, 1, 3, 9, 1, 19, 1, 5, 1, 3, 7, 21, 1, 11, 1, 23, 1, 3, 1, 5, 25, 1, 13, 1, 3, 9, 27, 1, 7, 1, 29, 1, 3, 5, 15, 1, 31, 1, 1, 3, 11, 33, 1, 17, 1, 5, 7, 35, 1
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 30 2012

Keywords

Comments

n-th row = intersection of A005408 and of n-th row of A027750.

Examples

			The triangle begins:
.  1   {1}
.  2   {1}
.  3   {1,3}
.  4   {1}
.  5   {1,5}
.  6   {1,3}
.  7   {1,7}
.  8   {1}
.  9   {1,3,9}
. 10   {1,5}
. 11   {1,11}
. 12   {1,3}
. 13   {1,13}
. 14   {1,7}
. 15   {1,3,5,15}
. 16   {1} .

Links

Crossrefs

Cf. A001227 (row lengths), A000593 (row sums), A136655 (row products).
Cf. A000265, A005408, A027750, A050999, A051000, A037283, A037284, A037285, A171565.
Cf. also A237048.

Programs

  • Haskell
    a182469 n k = a182469_tabf !! (n-1) !! (k-1)
a182469_row = a027750_row . a000265
a182469_tabf = map a182469_row [1..]
  • Mathematica
    Flatten[Table[Select[Divisors[n],OddQ],{n,40}]] (* Harvey P. Dale, Aug 13 2012 *)
Flatten[Table[Divisors[n / 2^IntegerExponent[n, 2]], {n, 40}]] (* Amiram Eldar, May 02 2025 *)
  • PARI
    tabf(nn) = {for (n=1, nn, fordiv(n, d, if (d%2, print1(d, ", "))); print(););} \\ Michel Marcus, Apr 22 2017
  • PARI
    row(n) = divisors(n >> valuation(n, 2)); \\ Amiram Eldar, May 02 2025
  • Python
    from sympy import divisors
def row(n):
    return [d for d in divisors(n) if d % 2]
for n in range(1, 21): print(row(n)) # Indranil Ghosh, Apr 22 2017

Formula

T(n,k) = A027750(A000265(n),k), 1 <= k <= A001227(n).
A000265(n) = T(n,A001227(n)).

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

A037285 Replace n with concatenation of its nontrivial odd divisors.

Original entry on oeis.org

0, 0, 0, 0, 0, 3, 0, 0, 3, 5, 0, 3, 0, 7, 35, 0, 0, 39, 0, 5, 37, 11, 0, 3, 5, 13, 39, 7, 0, 3515, 0, 0, 311, 17, 57, 39, 0, 19, 313, 5, 0, 3721, 0, 11, 35915, 23, 0, 3, 7, 525, 317, 13, 0, 3927, 511, 7, 319, 29, 0, 3515, 0, 31, 37921, 0, 513, 31133, 0, 17, 323, 5735, 0, 39, 0
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A182469, A209229, A010051, A106708, A037283, A037284.

Programs

  • Haskell
    import Data.List (delete)
a037285 n
| a209229 n == 1 = 0
| a010051 n == 1 = 0
| otherwise = read $ concat $ (map show) $ delete n $ tail $ a182469_row n
-- Reinhard Zumkeller, May 01 2012
  • Python
    from sympy import divisors
def a(n):
  nontrivial_odd_divisors = [d for d in divisors(n)[1:-1] if d%2 == 1]
  if len(nontrivial_odd_divisors) == 0: return 0
  else: return int("".join(str(d) for d in nontrivial_odd_divisors))
print([a(n) for n in range(1, 70)]) # Michael S. Branicky, Dec 31 2020

Extensions

More terms from Erich Friedman
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.