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- #!/usr/bin/perl
- # a(n) is the smallest centered triangular number with exactly n prime factors (counted with multiplicity).
- # https://oeis.org/A358929
- # Known terms:
- # 1, 19, 4, 316, 136, 760, 64, 4960, 22144, 103360, 27136, 5492224, 1186816, 41414656, 271212544, 559980544, 1334788096, 12943360, 7032930304, 527049293824, 158186536960, 1096295120896
- use 5.020;
- use warnings;
- use ntheory qw(:all);
- use experimental qw(signatures);
- # PARI/GP program:
- # a(n) = for(k=0, oo, my(t=3*k*(k+1)/2 + 1); if(bigomega(t) == n, return(t))); \\ ~~~~
- sub a($n) {
- for(my $k = 0; ;++$k) {
- my $v = divint(mulint(3*$k, ($k + 1)), 2) + 1;
- if (is_almost_prime($n, $v)) {
- return $v;
- }
- }
- }
- foreach my $n(1..100) {
- say "a($n) = ", a($n);
- }
- __END__
- a(1) = 19
- a(2) = 4
- a(3) = 316
- a(4) = 136
- a(5) = 760
- a(6) = 64
- a(7) = 4960
- a(8) = 22144
- a(9) = 103360
- a(10) = 27136
- a(11) = 5492224
- a(12) = 1186816
- a(13) = 41414656
- a(14) = 271212544
- a(15) = 559980544
- a(16) = 1334788096
- a(17) = 12943360
- a(18) = 7032930304
- a(19) = 527049293824
- a(20) = 158186536960
- a(21) = 1096295120896
- a(22) = 7871801589760
- a(23) = 154690378792960
- a(24) = 13071965224960
- a(25) = 56262393856
- a(26) = 964655941943296
- a(27) = 412520972025856
- a(28) = 20756701338664960
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