A124033 -id:A124033 - cp's OEIS frontend

A036335 Total number of composite numbers with n digits and n prime factors (counted with multiplicity).

0, 31, 225, 1563, 10222, 63030, 374264, 2160300, 12196405, 67724342, 371233523, 2014305995

Offset: 1

Patrick De Geest, Dec 15 1998

Essentially the same as A124033.

			a(1) = 0, since any single-digit number with 1 prime factor is a prime!

Carlos Rivera, Puzzle 25. Composed primes (by G.L. Honaker, Jr.), The Prime Puzzles and Problems Connection. (A related puzzle.)

Cf. A036336, A036337, A036338.

Table[Total[Table[If[CompositeQ[n]&&PrimeOmega[n]==x,1,0],{n,10^(x-1),10^x-1}]],{x,8}] (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Jun 19 2022 *)

One more term from Naohiro Nomoto, Jul 31 2001

a(9)-a(12) from Ray Chandler, Apr 12 2011

A175990 Irregular triangle read by rows: t(n,m) = binomial(n-m-1,m+1) for 0 <= m <= floor((n-1)/2).

Original entry on oeis.org

1, 2, 0, 3, 1, 4, 3, 0, 5, 6, 1, 6, 10, 4, 0, 7, 15, 10, 1, 8, 21, 20, 5, 0, 9, 28, 35, 15, 1, 10, 36, 56, 35, 6, 0, 11, 45, 84, 70, 21, 1, 12, 55, 120, 126, 56, 7, 0, 13, 66, 165, 210, 126, 28, 1, 14, 78, 220, 330, 252, 84, 8, 0, 15, 91, 286, 495, 462, 210, 36, 1, 16, 105, 364, 715, 792, 462, 120, 9, 0, 17, 120

Offset: 2

Roger L. Bagula, Dec 06 2010

			Triangle begins:
   1;
   2,  0;
   3,  1;
   4,  3,  0;
   5,  6,  1;
   6, 10,  4,  0;
   7, 15, 10,  1;
   8, 21, 20,  5,  0;
   9, 28, 35, 15,  1;
  10, 36, 56, 35,  6,  0;
  11, 45, 84, 70, 21,  1;

Row sums are A000071.
Essentially the same as A011973 (removing first column). Elimination of each 2nd row yields essentially A054142 or A121314. Interleaving with zeros gives A052553.
Padding with an initial column of 1's and more zeros yields A169803. Signed variants are A115139 and A124033.

Table[Binomial[n-m-1,m+1],{n,2,15},{m,0,Floor[(n-1)/2]}]//Flatten (* Harvey P. Dale, May 08 2023 *)

Definition clarified by Harvey P. Dale, May 08 2023

cp's OEIS Frontend

A036335 Total number of composite numbers with n digits and n prime factors (counted with multiplicity).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions