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- #!/usr/bin/perl
- # a(n) is the least number k such that sigma(sigma(k) * k) > n * sigma(k) * k.
- # https://oeis.org/A368063
- # Known terms:
- # 1, 2, 3, 10, 160, 12155, 26558675
- use 5.036;
- use ntheory;
- use Math::Prime::Util::GMP qw(:all);
- # a(7) <= 170075897311710390
- # a(7) <= 25811934519240870
- # a(7) <= 4163215245038850
- # a(7) <= 2928046583754721
- # a(7) <= 2458279478022940
- # a(7) <= 1989452141444911
- # a(7) <= 767320250907925
- # a(7) <= 121155829090725
- # a(7) <= 114775357632650
- # a(8) <= 272113056574982766111055794421
- # sigma(sigma(k) * k) > n * sigma(k) * k.
- #my $prod = vecprod(5, 11, 13, 17, 19, 23, 29, 31, 37);
- #my $prod = vecprod(5, 11, 13, 17, 19, 23, 29);
- #my $prod = 2928046583754721;
- #my $prod = vecprod(11, 13, 17, 19, 23, 29, 31, 41, 43, 73);
- #my $prod = vecprod(11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, );
- #my $prod = vecprod(11, 11, 13, 17, 23, 29, 47, 47);
- my $n = 7;
- my $prod = 223092870 * 73;
- foreach my $j (1..1e9) {
- my $k = ntheory::mulint($prod, $j);
- my $sigma = sigma($k);
- my $v = mulint($sigma, $k);
- if (sigma($v) > mulint($n, $v)) {
- die "Found: a($n) <= $k\n";
- }
- }
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