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.

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)).

A037283 Replace n with concatenation of its odd divisors.

Original entry on oeis.org

1, 1, 13, 1, 15, 13, 17, 1, 139, 15, 111, 13, 113, 17, 13515, 1, 117, 139, 119, 15, 13721, 111, 123, 13, 1525, 113, 13927, 17, 129, 13515, 131, 1, 131133, 117, 15735, 139, 137, 119, 131339, 15, 141, 13721, 143, 111, 13591545, 123, 147, 13, 1749, 1525, 131751
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A182469, A037278, A037284, A037285.

Programs

  • Haskell
    a037283 = read . concat . (map show) . a182469_row :: Integer -> Integer
-- Reinhard Zumkeller, May 01 2012
  • Mathematica
    dtn[ L_ ] := Fold[ 10#1+#2&, 0, L ] Array[ dtn[ Flatten[ Map[ IntegerDigits, Select[ Divisors[ # ], OddQ ] ] ] ]&, 50 ]
cod[n_]:=FromDigits[Flatten[IntegerDigits/@Select[Divisors[n],OddQ]]]; Array[cod,60] (* Harvey P. Dale, Jan 24 2014 *)
  • Python
    from sympy import divisors
def a(n): return int("".join(str(d) for d in divisors(n) if d%2==1))
print([a(n) for n in range(1, 52)]) # Michael S. Branicky, Dec 31 2020

Extensions

More terms from Erich Friedman

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

A037277 Replace n with concatenation of its divisors >1.

Original entry on oeis.org

0, 2, 3, 24, 5, 236, 7, 248, 39, 2510, 11, 234612, 13, 2714, 3515, 24816, 17, 236918, 19, 2451020, 3721, 21122, 23, 234681224, 525, 21326, 3927, 2471428, 29, 2356101530, 31, 2481632, 31133, 21734, 5735, 23469121836, 37, 21938, 31339
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A027750, A037284, A037278, A106708.

Programs

  • Haskell
    a037277 1 = 0
a037277 n = read $ concat $ map show $ tail $ a027750_row n
-- Reinhard Zumkeller, May 01 2012, Feb 07 2011
  • Mathematica
    FromDigits[Flatten[IntegerDigits/@Rest[Divisors[#]]]]&/@Range[40] (* Harvey P. Dale, Nov 06 2011 *)
  • Python
    from sympy import divisors
def a(n):
  divisors_gt1 = divisors(n)[1:]
  if len(divisors_gt1) == 0: return 0
  else: return int("".join(str(d) for d in divisors_gt1))
print([a(n) for n in range(1, 40)]) # 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.

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