login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Least prime factor of powers of semiprimes.
2

%I #12 Mar 04 2017 13:50:09

%S 1,2,2,3,2,2,3,2,3,2,5,2,3,2,5,2,2,3,2,7,3,5,3,2,2,2,5,3,2,7,3,2,5,2,

%T 3,7,3,2,5,2,2,3,5,2,7,11,2,3,3,7,2,3,2,11,5,2,5,2,3,7,2,13,3,2,3,5,

%U 11,2,2,3,2,7,5,2,11,3,2,5,2,7,2,3,13,3,2,5,3,13

%N Least prime factor of powers of semiprimes.

%H Michael De Vlieger, <a href="/A122443/b122443.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A020639(A085155(n)) = least prime factor of A085155 powers of semiprimes.

%t FactorInteger[#][[1, 1]] & /@ Select[Range@ 250, Function[n, Or[n == 1, And[Length@ # == 1, EvenQ@ First@ #], And[Length@ # == 2, SameQ @@ #]] &[FactorInteger[n][[All, -1]]]]] (* _Michael De Vlieger_, Mar 04 2017 *)

%o (PARI) is(n)=my(f=factor(n)[, 2]); #f==0 || (#f==2 && f[1]==f[2]) || (#f==1 && f[1]%2==0);

%o spf(n) = if (n==1, 1, factor(n)[1,1]);

%o lista(nn) = {for (n=1, nn, if (is(n), print1(spf(n), ", ")););} \\ _Michel Marcus_, Mar 04 2017

%Y Cf. A000040, A001358, A020639, A076396, A085155.

%Y Cf. A122444 (greatest prime factor of powers of semiprimes).

%Y Cf. A076396 (smallest prime factor of n-th perfect power).

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Sep 06 2006

%E More terms from _Michel Marcus_, Mar 04 2017