A348477 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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