A037285 -id:A037285 - cp's OEIS frontend

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

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

Reinhard Zumkeller, Apr 30 2012

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

			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} .

Reinhard Zumkeller, Rows n = 1..2500 of triangle, flattened

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

a182469 n k = a182469_tabf !! (n-1) !! (k-1)
a182469_row = a027750_row . a000265
a182469_tabf = map a182469_row [1..]

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 *)

tabf(nn) = {for (n=1, nn, fordiv(n, d, if (d%2, print1(d, ", "))); print(););} \\ Michel Marcus, Apr 22 2017

row(n) = divisors(n >> valuation(n, 2)); \\ Amiram Eldar, May 02 2025

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

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

A000265(n) = T(n,A001227(n)).

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

N. J. A. Sloane, Jul 20 2007

Klaus Brockhaus, Table of n, a(n) for n=1..5000

Cf. A037278, A120712, A037279, A131983 (records), A131984 (where records occur).

Cf. A027750, A010051, A037285, A037277, A163870.

a106708 1           = 0
a106708 n
   | a010051 n == 1 = 0
   | otherwise = read $ concat $ (map show) $ init $ tail $ a027750_row n
-- Reinhard Zumkeller, May 01 2012

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

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 *)

{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 */

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

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

More terms from R. J. Mathar and Klaus Brockhaus, Aug 01 2007

Name edited by Michael S. Branicky, Dec 31 2020

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

N. J. A. Sloane

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A182469, A037278, A037284, A037285.

a037283 = read . concat . (map show) . a182469_row :: Integer -> Integer
-- Reinhard Zumkeller, May 01 2012

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 *)

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

More terms from Erich Friedman

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

N. J. A. Sloane

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

a037284 n
   | a209229 n == 1 = 0
   | otherwise      = read $ concat $ (map show) $ tail $ a182469_row n
-- Reinhard Zumkeller, May 01 2012

Array[FromDigits[Flatten[IntegerDigits/@Rest[Select[Divisors[#], OddQ]]]]&, 60] (* Harvey P. Dale, Mar 03 2014 *)

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

a(36) corrected by Reinhard Zumkeller, May 01 2012

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

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

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A037283 Replace n with concatenation of its odd divisors.

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

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Haskell

Mathematica

Python

Extensions