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- #!/usr/bin/perl
- # a(n) is the smallest n-gonal number with exactly n prime factors (counted with multiplicity).
- # https://oeis.org/A358863
- # Known terms:
- # 28, 16, 176, 4950, 8910, 1408, 346500, 277992, 7542080, 326656, 544320, 120400000, 145213440, 48549888, 4733575168, 536813568, 2149576704, 3057500160, 938539560960, 1358951178240
- use 5.020;
- use ntheory qw(:all);
- use experimental qw(signatures);
- # PARI/GP program:
- # a(n) = if(n<3, return()); for(k=1, oo, my(t=(k*(n*k - n - 2*k + 4))\2); if(bigomega(t) == n, return(t)));
- # PARI/GP program for A359014:
- # a(n) = if(n<3, return()); for(k=1, oo, my(t=(k*(n*k - n - 2*k + 4))\2); if(bigomega(t) == n, return(k)));
- sub a($n) {
- for(my $k = 1; ; ++$k) {
- #my $t = divint(mulint($k, ($n*$k - $n - 2*$k + 4)), 2);
- my $t = rshiftint(mulint($k, ($n*$k - $n - 2*$k + 4)), 1);
- #my $t = ($k * ($n*$k - $n - 2*$k + 4))>>1;
- #if (prime_bigomega($t) == $n) {
- if (is_almost_prime($n, $t)) {
- return $t;
- }
- }
- }
- foreach my $n (3..100) {
- say "a($n) = ", a($n);
- }
- __END__
- a(3) = 28
- a(4) = 16
- a(5) = 176
- a(6) = 4950
- a(7) = 8910
- a(8) = 1408
- a(9) = 346500
- a(10) = 277992
- a(11) = 7542080
- a(12) = 326656
- a(13) = 544320
- a(14) = 120400000
- a(15) = 145213440
- a(16) = 48549888
- a(17) = 4733575168
- a(18) = 536813568
- a(19) = 2149576704
- a(20) = 3057500160
- a(21) = 938539560960
- a(22) = 1358951178240
- a(23) = 36324805836800
- a(24) = 99956555776
- a(25) = 49212503949312
- a(26) = 118747221196800
- a(27) = 59461613912064
- a(28) = 13749193801728
- a(29) = 7526849672380416
- a(30) = 98516240758210560
- a(31) = 4969489493917696
- a(32) = 78673429816934400
- a(33) = 4467570822566903808
- a(34) = 1013309912383488000
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