A122443 Least prime factor of powers of semiprimes.

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, 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, 11, 2, 2, 3, 2, 7, 5, 2, 11, 3, 2, 5, 2, 7, 2, 3, 13, 3, 2, 5, 3, 13

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

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

Mathematica

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 *)

Prog

(PARI) is(n)=my(f=factor(n)[, 2]); #f==0 || (#f==2 && f[1]==f[2]) || (#f==1 && f[1]%2==0);
spf(n) = if (n==1, 1, factor(n)[1, 1]);
lista(nn) = {for (n=1, nn, if (is(n), print1(spf(n), ", ")); ); } \\ Michel Marcus, Mar 04 2017

Crossrefs

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

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

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

Sequence in context: A046028 A330406 A125954 * A262945 A309674 A270516

Adjacent sequences: A122440 A122441 A122442 * A122444 A122445 A122446

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 06 2006

Extensions

More terms from Michel Marcus, Mar 04 2017

Status

approved