|
%I #19 Aug 04 2024 03:01:17
%S 0,1,1,2,1,1,1,3,2,1,1,1,2,1,1,1,4,1,1,2,1,1,2,1,1,1,1,3,2,1,3,1,2,1,
%T 1,1,5,1,1,1,2,1,1,1,1,3,1,1,1,1,2,1,2,1,1,1,4,2,1,2,1,1,2,1,1,3,1,1,
%U 3,1,1,1,1,2,1,1,1,2,6,1,1,1,1,2,1,1
%N Irregular triangle read by rows: row n contains the distinct values (in numerical order) making up the nonzero exponents in the prime factorization of n. (Row 1 = (0).).
%C Row n, for n>=2, contains A071625(n) terms.
%H Harvey P. Dale, <a href="/A136568/b136568.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>.
%e 4200 = 2^3 * 3^1 * 5^2 * 7^1. The exponents of the prime factorization are therefore 3,1,2,1. Therefore row 4200 is (1,2,3).
%e Table begins:
%e 0;
%e 1;
%e 1;
%e 2;
%e 1;
%e 1;
%e 1;
%e 3;
%e 2;
%e 1;
%e 1;
%e 1, 2;
%t Join[{0},Flatten[Rest[Table[Union[Transpose[FactorInteger[n]][[2]]],{n,100}]]]] (* _Harvey P. Dale_, Mar 19 2013 *)
%o (PARI) row(n) = if(n == 1, [0], Set(factor(n)[,2])); \\ _Amiram Eldar_, Aug 04 2024
%Y Cf. A071625, A136565.
%K nonn,tabf
%O 1,4
%A _Leroy Quet_, Jan 07 2008
%E More terms from _Harvey P. Dale_, Mar 19 2013
|
