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- #!/usr/bin/perl
- # a(n) is the smallest centered n-gonal number with exactly n prime factors (counted with multiplicity).
- # https://oeis.org/A358926
- # Known terms:
- # 316, 1625, 456, 3964051, 21568, 6561, 346528
- # PARI/GP program:
- # a(n) = if(n<3, return()); for(k=1, oo, my(t=((n*k*(k+1))/2+1)); if(bigomega(t) == n, return(t))); \\ ~~~~
- use 5.020;
- use warnings;
- use ntheory qw(:all);
- use experimental qw(signatures);
- sub a($n) {
- for(my $k = 1; ;++$k) {
- my $v = divint(mulint($n*$k, ($k + 1)), 2) + 1;
- if (is_almost_prime($n, $v)) {
- return $v;
- }
- }
- }
- foreach my $n(3..100) {
- say "a($n) = ", a($n);
- }
- __END__
- a(3) = 316
- a(4) = 1625
- a(5) = 456
- a(6) = 3964051
- a(7) = 21568
- a(8) = 6561
- a(9) = 346528
- a(10) = 3588955448828761
- a(11) = 1684992
- a(12) = 210804461608463437
- a(13) = 36865024
- a(14) = 835904150390625
- a(15) = 2052407296
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