A062825 -id:A062825 - cp's OEIS frontend

A163870 Triangle read by rows: row n lists the nontrivial divisors of the n-th composite.

2, 2, 3, 2, 4, 3, 2, 5, 2, 3, 4, 6, 2, 7, 3, 5, 2, 4, 8, 2, 3, 6, 9, 2, 4, 5, 10, 3, 7, 2, 11, 2, 3, 4, 6, 8, 12, 5, 2, 13, 3, 9, 2, 4, 7, 14, 2, 3, 5, 6, 10, 15, 2, 4, 8, 16, 3, 11, 2, 17, 5, 7, 2, 3, 4, 6, 9, 12, 18, 2, 19, 3, 13, 2, 4, 5, 8, 10, 20, 2, 3, 6, 7, 14, 21, 2, 4, 11, 22, 3, 5, 9, 15, 2, 23

Offset: 1

Juri-Stepan Gerasimov, Aug 06 2009

Row n contains row A002808(n) of table A027750.

T(n,k) = A027751(A002808(n),k+1), k = 1..A144925(n). - Reinhard Zumkeller, Mar 29 2014

			The table starts in row n=1 (with the composite 4) as
  2;
  2,3;
  2,4;
  3;
  2,5;
  2,3,4,6;
  2,7;
  3,5;
  2,4,8;
  2,3,6,9;
  2,4,5,10.

Reinhard Zumkeller, Rows n = 1..1000 of table, flattened

Cf. A002808, A027750.

Cf. A144925 (row lengths), A062825 (row sums), A056608 (left edge), A160180 (right edge).

a163870 n k = a163870_tabf !! (n-1) !! (k-1)
a163870_row n = a163870_tabf !! (n-1)
a163870_tabf = filter (not . null) $ map tail a027751_tabf
-- Reinhard Zumkeller, Mar 29 2014

Divisors[Select[Range[50], CompositeQ]][[All, 2 ;; -2]] (* Paolo Xausa, Dec 26 2024 *)

from itertools import islice
def g():
    n, j = 1, 2
    while True:
        n = (n << 1) | 1
        p = 1
        for k in range(2, (j >> 1) + 1):
            p = (p << 1) | 1
            if n % p == 0: yield k
        j+=1
print(list(islice(g(),95))) # Darío Clavijo, Dec 16 2024

Entries checked by R. J. Mathar, Sep 22 2009

A163871 The n-th composite plus the sum of its nontrivial divisors.

Original entry on oeis.org

6, 11, 14, 12, 17, 27, 23, 23, 30, 38, 41, 31, 35, 59, 30, 41, 39, 55, 71, 62, 47, 53, 47, 90, 59, 55, 89, 95, 83, 77, 71, 123, 56, 92, 71, 97, 119, 71, 119, 79, 89, 167, 95, 103, 126, 83, 143, 125, 95, 143, 194, 113, 123, 139, 95, 167, 185, 120, 125, 223, 107, 131, 119, 179

Offset: 1

Juri-Stepan Gerasimov, Aug 06 2009

Trivial divisors of a number are 1 and the number itself, see A048050.

			a(1) = 4 + 2 =  6;
a(2) = 6 + 5 = 11;
a(3) = 8 + 6 = 14.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A027750.

A002808 := proc(n) local resul,i ; i := 1 ; resul := 4 ; while i < n do resul := resul+1 ; while isprime(resul) do resul := resul+1 ; od ; i := i+1 ; od; RETURN(resul) ; end:
A048050 := proc(n) if n <= 3 then 0; else numtheory[sigma](n)-n-1 ; fi; end:
A163871 := proc(n) A002808(n)+A048050(A002808(n)) ; end: seq(A163871(n),n=1..80) ; # R. J. Mathar, Aug 11 2009

#+Total[Most[Rest[Divisors[#]]]]&/@Select[Range[4,200],!PrimeQ[#]&] (* Harvey P. Dale, Oct 28 2013 *)

a(n) = A002808(n) + A062825(n+1).

a(4) corrected by R. J. Mathar, Aug 11 2009

cp's OEIS Frontend

A163870 Triangle read by rows: row n lists the nontrivial divisors of the n-th composite.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

Python

Extensions