Kevin Ryde > Math-NumSeq-65 > Math::NumSeq::PowerFlip
Annotate this POD    Open  0 View/Report Bugs Module Version: 65
  Source   Latest Release: Math-NumSeq-69
Math::NumSeq::PowerFlip -- prime exponent flip    use
Math::NumSeq::PowerFlip;  my $seq =
Math::NumSeq::PowerFlip->new;   This sequence is i with primes
and exponents flipped in the prime factorization.      i     =
p^e * q^f * ...     value = e^p * f^q * ...  which gives      1,
1, 1, 4, 1, 1, 1, 9, 8, 1, 1, 4, 1, 1, 1, 16, 1, 8, 1, 4, ...
starting i=1  For example i=1000=2^3*5^3 becomes
value=3^2*3^5=3^7=2187.  Any i=prime has value=1 since i=p^1
becomes value=1^p=1. Value=1 occurs precisely when i=p*q*r*etc
with no repeated prime factor, ie. when i is square-free.  The
possible values which occur in the sequence are related to
square factors. Since value=e^p has prime p>=2, every e,f,g etc
powered up in the value is a square or higher power. So sequence
values are a product of squares and higher.     $seq =
Math::NumSeq::PowerFlip->new ()