A348477 Drop all 1 but the first 1 in A035306.

1, 2, 3, 2, 2, 5, 2, 3, 7, 2, 3, 3, 2, 2, 5, 11, 2, 2, 3, 13, 2, 7, 3, 5, 2, 4, 17, 2, 3, 2, 19, 2, 2, 5, 3, 7, 2, 11, 23, 2, 3, 3, 5, 2, 2, 13, 3, 3, 2, 2, 7, 29, 2, 3, 5, 31, 2, 5, 3, 11, 2, 17, 5, 7, 2, 2, 3, 2, 37, 2, 19, 3, 13, 2, 3, 5, 41, 2, 3, 7, 43, 2, 2, 11, 3, 2, 5, 2, 23, 47, 2, 4, 3, 7, 2, 2, 5, 2, 3, 17, 2, 2, 13, 53, 2, 3, 3, 5, 11, 2, 3, 7, 3, 19, 2, 29

Offset

1,2

Comments

List of prime divisors of n and their exponents, ignoring the exponent 1. - Michael De Vlieger, Oct 20 2021

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Prime Factorization.

Example

   n   prime factorization  triangle
   1 = 1.                 ->  1;
   2 = 2.                 ->  2;
   3 = 3.                 ->  3;
   4 = 2^2.               ->  2, 2;
   5 = 5.                 ->  5;
   6 = 2*3.               ->  2, 3;
   7 = 7.                 ->  7;
   8 = 2^3.               ->  2, 3;
   9 = 3^2.               ->  3, 2;
  10 = 2*5.               ->  2, 5;
  11 = 11.                -> 11;
  12 = 2^2*3.             ->  2, 2, 3;
  13 = 13.                -> 13;
  14 = 2*7                ->  2, 7;
  15 = 3*5.               ->  3, 5;
  16 = 2^4.               ->  2, 4;

Mathematica

Array[DeleteCases[Flatten@ FactorInteger[#], 1] &, 58] /. {} -> {1} // Flatten (* Michael De Vlieger, Oct 20 2021 *)

Prog

(PARI)
tabf(nn) = if(nn==1, print1(1, ", "), my(f=factor(nn)); for(i=1, #f~, for(j=1, 2, if((k=f[i, j])>j-1, print1(k, ", ")))));
(Ruby)
require 'prime'
def A348477(n)
  ary = (2..n).map{|i| i.prime_division}.flatten
  ary.delete(1)
  [1] + ary
end
p A348477(60)

Crossrefs

Column 1 is A020639.

Row lengths are A238949(n) for n > 1.

Cf. A027746, A035306.

Sequence in context: A207338 A027746 A307746 * A240230 A238689 A166454

Adjacent sequences: A348474 A348475 A348476 * A348478 A348479 A348480

Keyword

nonn,easy,tabf

Author

Seiichi Manyama, Oct 20 2021

Status

approved